Questions on Algebra: Linear Equations, Graphs, Slope answered by real tutors!

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Question 175650: solve and graph the following equation:
-x-5y=-8
: solve and graph the following equation:
-x-5y=-8

Answer by jim_thompson5910(9911)

(Show Source):

You can put this solution on YOUR website!
-x-5y=-8

Start with the given equation.

-5y=-8+x

Add

to both sides.

-5y=x-8

Rearrange the terms.

y=(x-8)/(-5)

Divide both sides by

to isolate y.

y=((1)/(-5))x+(-8)/(-5)

Break up the fraction.

y=-(1/5)x+8/5

Reduce.

In order to graph this equation, we only need two points to create a straight line

--------------------------------Let's find the first point--------------------------------

y=-(1/5)x+8/5

Start with the given equation

y=-(1/5)(3)+8/5

Plug in

Multiply

and

to get

Add

Reduce

So when x=3

, we have the value y=1

. This means we have the first point

--------------------------------Let's find the second point--------------------------------

y=-(1/5)x+8/5

Start with the given equation

y=-(1/5)(8)+8/5

Plug in

Multiply

and

to get

Add

Reduce

So when x=8

, we have the value y=0

. This means we have the second point

------------------------------------------------------------------------------------------------

So we have the two points:

and

Now plot these two points on a coordinate system

drawing(500,500,-4.5,15.5,-4.5,15.5, 
graph(500,500,-4.5,15.5,-4.5,15.5,0), 
grid(1), 
circle(3,5/5,0.1), 
circle(3,5/5,0.12), 
circle(3,5/5,0.15), 
circle(8,0/5,0.1), 
circle(8,0/5,0.12), 
circle(8,0/5,0.15) 
)

drawing(500,500,-4.5,15.5,-4.5,15.5,<BR>
graph(500,500,-4.5,15.5,-4.5,15.5,0),<BR>
grid(1),<BR>
circle(3,5/5,0.1),<BR>
circle(3,5/5,0.12),<BR>
circle(3,5/5,0.15),<BR>
circle(8,0/5,0.1),<BR>
circle(8,0/5,0.12),<BR>
circle(8,0/5,0.15)<BR>
)

Now draw a straight line through the two points. This line is the graph of y=-(1/5)x+8/5

drawing(500,500,-4.5,15.5,-4.5,15.5,<BR>
graph(500,500,-4.5,15.5,-4.5,15.5,-(1/5)x+8/5),<BR>
grid(1),<BR>
circle(3,5/5,0.1),<BR>
circle(3,5/5,0.12),<BR>
circle(3,5/5,0.15),<BR>
circle(8,0/5,0.1),<BR>
circle(8,0/5,0.12),<BR>
circle(8,0/5,0.15)<BR>
)

Graph of

through the two points

and

Question 175560: What is the slope and y intercept for the line in b?
b) The water line is given by the equation y=-2/3x-12
Suppose you want to put a pink flamingo lawn ornament in your backyard, but you want to avoid placing it directly over the water line, in case you need to excavate the line for repairs in the future. Could you place it at the point
(-4,-10)?
No
: What is the slope and y intercept for the line in b?
b) The water line is given by the equation y=-2/3x-12
Suppose you want to put a pink flamingo lawn ornament in your backyard, but you want to avoid placing it directly over the water line, in case you need to excavate the line for repairs in the future. Could you place it at the point
(-4,-10)?
No

Answer by jim_thompson5910(9911)

(Show Source):

You can put this solution on YOUR website!
We can see that the equation y=-(2/3)x-12

is in slope intercept form y=mx+b

where the slope is m=-2/3

and the y-intercept is b=-12

note: the y-intercept is the point

Since we're looking at the point (-4,-10), this means that x=-4

and

Start with the given equation.

-10=-(2/3)(-4)-12

Plug in

and

Multiply

Multiply 12 by 3/3

Subtract the fractions.

Since the equation is NOT true, this means that the point (-4,-10) is NOT on the line y=-(2/3)x-12

. So the flamingo at the point (-4,-10) is NOT on the water line y=-(2/3)x-12

So you can place the flamingo at the point (-4,-10).

Question 175557: Write an equation of the line that is parallel to the given line and passes through the given point.
A) y=x + 3. (5, 0)
B) y= 2x + 3. (-4,1)
: Write an equation of the line that is parallel to the given line and passes through the given point.
A) y=x + 3. (5, 0)
B) y= 2x + 3. (-4,1)

Answer by Mathtut(1331)

(Show Source):

You can put this solution on YOUR website!

A) the slope has to be the same to be parallel m the slope for y=x+3 is 1. Now we have the slope and a point. using the point slope formula
:
y-0=1(x-5)
:
highlight(y=x-5)

:
B)in y=2x+3 the slope is 2. using the point slope formula
:
y-1=2(x+4)
:
y-1=2x+8
:
highlight(y=2x+9)

Question 175553: y=-2/3x-12 (water line)
avoid placing lawn ornament over water line....could the water line be placed at (-4, -10)?
: y=-2/3x-12 (water line)
avoid placing lawn ornament over water line....could the water line be placed at (-4, -10)?

Answer by nycsub_teacher(90)

(Show Source):

You can put this solution on YOUR website!
Replace x with -4 and y with -10 in the given equation and then simplify.
If you get the same answer on both sides of the equation, then the answer is yes. If not, then answer is no.
Understand?
=================================
I received your e-mail. Yes, I also got no. Like I said, they give you a point. Each point has a value for x and y as you know. The question would like to know if the given point makes the equation true.
After replacing x and y with their value and simplifying the equation, we learn that the given point (-4, -10) does not get the same answer on both sides of the equation.
Understand?

Question 175535: write an equation of the line that has each pair of intercepts
x-intercept:3, y-intercept:3: write an equation of the line that has each pair of intercepts
x-intercept:3, y-intercept:3
Answer by Mathtut(1331)

(Show Source):

You can put this solution on YOUR website!
m=slope=rise/run= DELTA(y)/DELTA(x)

well you get the point
:
m=3-0/0-3=-1
:
y intercept 3
:
y=-x+3

Question 175510This question is from textbook prentice hall mathematics
: This question is from textbook prentice hall mathematics
:
Answer by Mathtut(1331)

(Show Source):

You can put this solution on YOUR website!
need a question!!! thanks

Question 175522: write an equation of the line that has each pair of intercepts
x-intercept:-1, y-intercept:4: write an equation of the line that has each pair of intercepts
x-intercept:-1, y-intercept:4
Answer by Mathtut(1331)

(Show Source):

You can put this solution on YOUR website!
you have two points and from 2 points you can find the slope m
:
4-0/0-(-1)=4
:
y intercept is 4
:
highlight(y=4x+4)

(Show Source):

You can put this solution on YOUR website!
See answer to Problem 175521. Do this one the same way.

http://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.175521.html

Question 175523: write an equation of the line that has each pair of intercepts
x-intercept:-4, y-intercept:-8: write an equation of the line that has each pair of intercepts
x-intercept:-4, y-intercept:-8
Answer by Mathtut(1331)

(Show Source):

You can put this solution on YOUR website!
m=slope =-8-0/0-(-4)=-8/-4=-2..... y intercept is -8
:
so highlight(y=-2x-8)

(Show Source):

You can put this solution on YOUR website!
See answer to Problem 175521. Do this one the same way.

http://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.175521.html

Question 175521: write an equation of the line that has each pair of intercepts
x-intercept:3, y-intercept:3: write an equation of the line that has each pair of intercepts
x-intercept:3, y-intercept:3
Answer by solver91311(2187)

(Show Source):

You can put this solution on YOUR website!
The x-intercept is the point where the y coordinate is zero. Likewise, the y-intercept is the point where the x coordinate is zero. Therefore the two points described are:

and

Now use the two-point form of the equation of a line:

y - y[1]=((y[1] - y[2])/(x[1] - x[2]))(x - x[1])

Just substitute and do the arithmetic:

y - 3=((3 - 0)/(0 - 3))(x - 0)

I'll let you do the arithmetic part.

Question 175495: Write a linear equation in the form y=mx+b givien the following information.
b) has a slope of 2/3 and passes through the point (12,3).
c) passes through the points (5,5) (-3,-1): Write a linear equation in the form y=mx+b givien the following information.
b) has a slope of 2/3 and passes through the point (12,3).
c) passes through the points (5,5) (-3,-1)
Answer by jim_thompson5910(9911)

(Show Source):

You can put this solution on YOUR website!
b)

If you want to find the equation of line with a given a slope of 2/3

which goes through the point (

), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---
y-y[1]=m(x-x[1])

where

is the slope, and

is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-3=(2/3)(x-12)

Plug in

, and

(these values are given)

y-3=(2/3)x+(2/3)(-12)

Distribute 2/3

Multiply

and

to get

Add 3 to both sides to isolate y

y=(2/3)x-5

Combine like terms

and

to get

------------------------------------------------------------------------------------------------------------
Answer:

So the equation of the line with a slope of 2/3

which goes through the point (

) is:

which is now in y=mx+b

form where the slope is m=2/3

and the y-intercept is b=-5

Notice if we graph the equation y=(2/3)x-5

and plot the point (

), we get (note: if you need help with graphing, check out this solver )

drawing(500, 500, -5, 15, -6, 12, 
graph(500, 500, -5, 15, -6, 12,(2/3)x+-5), 
circle(12,3,0.12), 
circle(12,3,0.12+0.03) 
)

drawing(500, 500, -5, 15, -6, 12,<BR>
graph(500, 500, -5, 15, -6, 12,(2/3)x+-5),<BR>
circle(12,3,0.12),<BR>
circle(12,3,0.12+0.03)<BR>
)

Graph of

through the point (

)
and we can see that the point lies on the line. Since we know the equation has a slope of 2/3

and goes through the point (

), this verifies our answer.

c)

First let's find the slope of the line through the points

and

Start with the slope formula.

m=(-1-5)/(-3-5)

Plug in

Reduce

So the slope of the line that goes through the points

and

Now let's use the point slope formula:

y-y[1]=m(x-x[1])

Start with the point slope formula

y-5=(3/4)(x-5)

Plug in

, and

Distribute

y-5=(3/4)x-15/4

Multiply

Add 5 to both sides.

y=(3/4)x+5/4

Combine like terms. note: If you need help with fractions, check out this solver.

y=(3/4)x+5/4

Simplify

So the equation that goes through the points

and

Notice how the graph of y=(3/4)x+5/4

goes through the points

and

. So this visually verifies our answer.
drawing( 500, 500, -10, 10, -10, 10, 
graph( 500, 500, -10, 10, -10, 10,(3/4)x+5/4), 
circle(5,5,0.08), 
circle(5,5,0.10), 
circle(5,5,0.12), 
circle(-3,-1,0.08), 
circle(-3,-1,0.10), 
circle(-3,-1,0.12) 
)

drawing( 500, 500, -10, 10, -10, 10,<BR>
graph( 500, 500, -10, 10, -10, 10,(3/4)x+5/4),<BR>
circle(5,5,0.08),<BR>
circle(5,5,0.10),<BR>
circle(5,5,0.12),<BR>
circle(-3,-1,0.08),<BR>
circle(-3,-1,0.10),<BR>
circle(-3,-1,0.12)<BR>
)

Graph of

through the points

and

Question 175487: Question: Write an equation of the line that has each pair of intercepts.
x-intercept:2, Y-intercept:-4 How do I do this?: Question: Write an equation of the line that has each pair of intercepts.
x-intercept:2, Y-intercept:-4 How do I do this?
Answer by jim_thompson5910(9911)

(Show Source):

You can put this solution on YOUR website!
x-intercept:2 tells us that the point (2,0) is on the line
y-intercept: -4 means that (0,-4) is on the line

So we need to find the equation of the line through the points (2,0) and (0,-4)

First let's find the slope of the line through the points

and

Start with the slope formula.

m=(-4-0)/(0-2)

Plug in

, and

Subtract

from

to get

Subtract

from

to get

Reduce

So the slope of the line that goes through the points

and

Now let's use the point slope formula:

y-y[1]=m(x-x[1])

Start with the point slope formula

y-0=2(x-2)

Plug in

, and

Distribute

y-0=2x-4

Multiply

Add 0 to both sides.

y=2x-4

Combine like terms.

y=2x-4

Simplify

So the equation that goes through the points

and

Notice how the graph of y=2x-4

goes through the points

and

. So this visually verifies our answer.
drawing( 500, 500, -10, 10, -10, 10, 
graph( 500, 500, -10, 10, -10, 10,2x-4), 
circle(2,0,0.08), 
circle(2,0,0.10), 
circle(2,0,0.12), 
circle(0,-4,0.08), 
circle(0,-4,0.10), 
circle(0,-4,0.12) 
)

drawing( 500, 500, -10, 10, -10, 10,<BR>
graph( 500, 500, -10, 10, -10, 10,2x-4),<BR>
circle(2,0,0.08),<BR>
circle(2,0,0.10),<BR>
circle(2,0,0.12),<BR>
circle(0,-4,0.08),<BR>
circle(0,-4,0.10),<BR>
circle(0,-4,0.12)<BR>
)

Graph of

through the points

and

Question 175488: Question: Write an equation of the ilne that passes through each point with the given slope. (-5,4),m=0: Question: Write an equation of the ilne that passes through each point with the given slope. (-5,4),m=0
Answer by jim_thompson5910(9911)

(Show Source):

You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of

which goes through the point (-5,4), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---
y-y[1]=m(x-x[1])

where

is the slope, and

is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-4=(0)(x--5)

Plug in

, and

(these values are given)

y-4=(0)(x+5)

Rewrite

Distribute

Multiply

and

to get

Multiply

and

to get

Add 4 to both sides to isolate y

y=4

Combine like terms.
------------------------------------------------------------------------------------------------------------
Answer:

So the equation of the line with a slope of

which goes through the point (

) is:

which is now in y=mx+b

form where the slope is m=0

and the y-intercept is b=4

Notice if we graph the equation y=4

and plot the point (-5,4), we get

drawing(500, 500, -14, 4, -5, 13, 
graph(500, 500, -14, 4, -5, 13,(0)x+4), 
circle(-5,4,0.12), 
circle(-5,4,0.12+0.03) 
)

Graph of

through the point (-5,4)
and we can see that the point lies on the line. Since we know the equation has a slope of

and goes through the point (-5,4), this verifies our answer.

Question 175490: Question: Write an equation of the line that passes through each point with the given slope. (-1,-3),m=5: Question: Write an equation of the line that passes through each point with the given slope. (-1,-3),m=5
Answer by jim_thompson5910(9911)

(Show Source):

You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of

which goes through the point (

), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---
y-y[1]=m(x-x[1])

where

is the slope, and

is the given point

So lets use the Point-Slope Formula to find the equation of the line

y--3=(5)(x--1)

Plug in

, and

(these values are given)

y+3=(5)(x--1)

Rewrite

Rewrite

Distribute

Multiply

and

to get

Subtract 3 from both sides to isolate y

y=5x+2

Combine like terms

and

to get

------------------------------------------------------------------------------------------------------------
Answer:

So the equation of the line with a slope of

which goes through the point (

) is:

which is now in y=mx+b

form where the slope is m=5

and the y-intercept is b=2

Notice if we graph the equation y=5x+2

and plot the point (

), we get (note: if you need help with graphing, check out this solver )

drawing(500, 500, -10, 8, -12, 6, 
graph(500, 500, -10, 8, -12, 6,(5)x+2), 
circle(-1,-3,0.12), 
circle(-1,-3,0.12+0.03) 
)

drawing(500, 500, -10, 8, -12, 6,<BR>
graph(500, 500, -10, 8, -12, 6,(5)x+2),<BR>
circle(-1,-3,0.12),<BR>
circle(-1,-3,0.12+0.03)<BR>
)

Graph of

through the point (

)
and we can see that the point lies on the line. Since we know the equation has a slope of

and goes through the point (

), this verifies our answer.

Question 175491: Question: Write an equation of the line that passes through each point with the given slope. (1,-4),m=-6: Question: Write an equation of the line that passes through each point with the given slope. (1,-4),m=-6
Answer by jim_thompson5910(9911)

(Show Source):

You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of

which goes through the point (

), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---
y-y[1]=m(x-x[1])

where

is the slope, and

is the given point

So lets use the Point-Slope Formula to find the equation of the line

y--4=(-6)(x-1)

Plug in

, and

(these values are given)

y+4=(-6)(x-1)

Rewrite

Distribute

Multiply

and

to get

Subtract 4 from both sides to isolate y

y=-6x+2

Combine like terms

and

to get

------------------------------------------------------------------------------------------------------------
Answer:

So the equation of the line with a slope of

which goes through the point (

) is:

which is now in y=mx+b

form where the slope is m=-6

and the y-intercept is b=2

Notice if we graph the equation y=-6x+2

and plot the point (

), we get (note: if you need help with graphing, check out this solver )

drawing(500, 500, -8, 10, -13, 5, 
graph(500, 500, -8, 10, -13, 5,(-6)x+2), 
circle(1,-4,0.12), 
circle(1,-4,0.12+0.03) 
)

drawing(500, 500, -8, 10, -13, 5,<BR>
graph(500, 500, -8, 10, -13, 5,(-6)x+2),<BR>
circle(1,-4,0.12),<BR>
circle(1,-4,0.12+0.03)<BR>
)

Graph of

through the point (

)
and we can see that the point lies on the line. Since we know the equation has a slope of

and goes through the point (

), this verifies our answer.

Question 175489: Question: Write an equation of the line that passes through each point with the given slope. (2,2),m=1/2: Question: Write an equation of the line that passes through each point with the given slope. (2,2),m=1/2
Answer by jim_thompson5910(9911)

(Show Source):

You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of 1/2

which goes through the point (

), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---
y-y[1]=m(x-x[1])

where

is the slope, and

is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-2=(1/2)(x-2)

Plug in

, and

(these values are given)

y-2=(1/2)x+(1/2)(-2)

Distribute 1/2

Multiply

and

to get

Add 2 to both sides to isolate y

y=(1/2)x+1

Combine like terms

and

to get

------------------------------------------------------------------------------------------------------------
Answer:

So the equation of the line with a slope of 1/2

which goes through the point (

) is:

which is now in y=mx+b

form where the slope is m=1/2

and the y-intercept is b=1

Notice if we graph the equation y=(1/2)x+1

and plot the point (

), we get (note: if you need help with graphing, check out this solver )

drawing(500, 500, -7, 11, -7, 11, 
graph(500, 500, -7, 11, -7, 11,(1/2)x+1), 
circle(2,2,0.12), 
circle(2,2,0.12+0.03) 
)

drawing(500, 500, -7, 11, -7, 11,<BR>
graph(500, 500, -7, 11, -7, 11,(1/2)x+1),<BR>
circle(2,2,0.12),<BR>
circle(2,2,0.12+0.03)<BR>
)

Graph of

through the point (

)
and we can see that the point lies on the line. Since we know the equation has a slope of 1/2

and goes through the point (

), this verifies our answer.

Question 175485: Write an equation of the line that has each pair of intercepts:
X-intercept:1, Y-intercept:2: Write an equation of the line that has each pair of intercepts:
X-intercept:1, Y-intercept:2
Answer by jim_thompson5910(9911)

(Show Source):

You can put this solution on YOUR website!
X-intercept:1 means that the point (1,0) is on the line

Y-intercept:2 means that the point (0,2) is on the line

So let's find the equation of the line through the points (1,0) and (0,2)

First let's find the slope of the line through the points

and

Start with the slope formula.

m=(2-0)/(0-1)

Plug in

, and

Subtract

from

to get

Subtract

from

to get

Reduce

So the slope of the line that goes through the points

and

Now let's use the point slope formula:

y-y[1]=m(x-x[1])

Start with the point slope formula

y-0=-2(x-1)

Plug in

, and

Simplify

Distribute

y=-2x+2

Multiply

So the equation that goes through the points

and

Notice how the graph of y=-2x+2

goes through the points

and

. So this visually verifies our answer.
drawing( 500, 500, -10, 10, -10, 10, 
graph( 500, 500, -10, 10, -10, 10,-2x+2), 
circle(1,0,0.08), 
circle(1,0,0.10), 
circle(1,0,0.12), 
circle(0,2,0.08), 
circle(0,2,0.10), 
circle(0,2,0.12) 
)

drawing( 500, 500, -10, 10, -10, 10,<BR>
graph( 500, 500, -10, 10, -10, 10,-2x+2),<BR>
circle(1,0,0.08),<BR>
circle(1,0,0.10),<BR>
circle(1,0,0.12),<BR>
circle(0,2,0.08),<BR>
circle(0,2,0.10),<BR>
circle(0,2,0.12)<BR>
)

Graph of

through the points

and

Question 175480: i need help doing this problem:
-3a + b = 4
-9a + 5b = -1
need this answered tonight!!! thank you!!
(this is a really neat place!!): i need help doing this problem:
-3a + b = 4
-9a + 5b = -1
need this answered tonight!!! thank you!!
(this is a really neat place!!)
Answer by Mathtut(1331)

(Show Source):

You can put this solution on YOUR website!
this is a system of equation that we will solve similtaneously
:
-3a + b = 4 ....eq 1
-9a + 5b = -1...eq 2
:
multiply eq 1 by -3
:
9a-3b=-12....revised eq 1
-9a+5b=-1....eq 2
:
I lined the 2 equations up so you can see that when we add the equations together the a terms are eliminated because 9a-9a=0. We are left with
-3b+5b=-12-1.
:
2b=-13
:
highlight(b=-13/2)

:
now take b's found value and plug it back into either equation. I will use eq 1
:
-3a + (-13/2)=4 ........now multiply all terms by 2 to get rid of fraction
:
-6a-13=8
:
-6a=21
:
highlight(a=-21/6=-7/2)

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Start with the given system of equations:
system(-3a+b=4,-9a+5b=-1)

Multiply the both sides of the first equation by -3.

9a-3b=-12

Distribute and multiply.

So we have the new system of equations:
system(9a-3b=-12,-9a+5b=-1)

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

(9a-3b)+(-9a+5b)=(-12)+(-1)

Group like terms.

0a+2b=-13

Combine like terms. Notice how the x terms cancel out.

2b=-13

Simplify.

Divide both sides by

to isolate

.

------------------------------------------------------------------

9a-3b=-12

Now go back to the first equation.

9a-3(-13/2)=-12

Plug in

Multiply.

Multiply both sides by the LCD

to clear any fractions.

18a+39=-24

Distribute and multiply.

18a=-24-39

Subtract

from both sides.

18a=-63

Combine like terms on the right side.

a=(-63)/(18)

Divide both sides by

to isolate

Reduce.

So our answer is a=-7/2

and

.

Which form the ordered pair

.

This means that the system is consistent and independent.

Question 175465: Write and equation in slope-intercept form of the line that passes through the given points such as (12,-3),(-8,1): Write and equation in slope-intercept form of the line that passes through the given points such as (12,-3),(-8,1)
Answer by jim_thompson5910(9911)

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You can put this solution on YOUR website!

First let's find the slope of the line through the points

and

Start with the slope formula.

m=(1--3)/(-8-12)

Plug in

, and

Subtract

from

to get

Subtract

from

to get

Reduce

So the slope of the line that goes through the points

and

Now let's use the point slope formula:

y-y[1]=m(x-x[1])

Start with the point slope formula

y--3=(-1/5)(x-12)

Plug in

, and

Rewrite

Distribute

y+3=(-1/5)x+12/5

Multiply

Subtract 3 from both sides.

y=(-1/5)x-3/5

Combine like terms. note: If you need help with fractions, check out this solver.

y=(-1/5)x-3/5

Simplify

So the equation that goes through the points

and

Notice how the graph of y=(-1/5)x-3/5

goes through the points

and

. So this visually verifies our answer.
drawing( 500, 500, -10, 13, -10, 10, 
graph( 500, 500, -10, 13, -10, 10,(-1/5)x-3/5), 
circle(12,-3,0.08), 
circle(12,-3,0.10), 
circle(12,-3,0.12), 
circle(-8,1,0.08), 
circle(-8,1,0.10), 
circle(-8,1,0.12) 
)

drawing( 500, 500, -10, 13, -10, 10,<BR>
graph( 500, 500, -10, 13, -10, 10,(-1/5)x-3/5),<BR>
circle(12,-3,0.08),<BR>
circle(12,-3,0.10),<BR>
circle(12,-3,0.12),<BR>
circle(-8,1,0.08),<BR>
circle(-8,1,0.10),<BR>
circle(-8,1,0.12)<BR>
)

Graph of

through the points

and

Question 175365: Find a real world example and formulate it into a linear equation. How do you interpret the slope and y intercept in your case?: Find a real world example and formulate it into a linear equation. How do you interpret the slope and y intercept in your case?
Answer by Mathtut(1331)

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The average lifespan of American women has been tracked, and the model for the data is y = 0.2t + 73, where t = 0 corresponds to 1960.
What is the slope? It is m = 0.2. This values tells me that, for every increase of 1 in my input variable t (that is, for every increase of one year), the value of my output variable y will increase by 0.2.

What is the meaning of the slope? It means that, every year, the average lifespan of American women increased by 0.2 years, or about 2.4 months.
When t = 0, what is the value of y? Looking at the equation, I see that y = 73.
What is the meaning of this y-value? It means that, in 1960 (when they started counting), the average lifespan of an American woman was 73 years.

Question 175268This question is from textbook Glencoe Algebra Concepts and Applications

: Determine whether the graphs of each pair of equations are parallel,perpendicular, or neither. 23) 7x+3y=4
3x-7y=1This question is from textbook Glencoe Algebra Concepts and Applications

: Determine whether the graphs of each pair of equations are parallel,perpendicular, or neither. 23) 7x+3y=4
3x-7y=1
Answer by jim_thompson5910(9911)

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7x+3y=4

Start with the first equation.

3y=4-7x

Subtract

from both sides.

3y=-7x+4

Rearrange the terms.

y=(-7x+4)/(3)

Divide both sides by

to isolate y.

y=((-7)/(3))x+(4)/(3)

Break up the fraction.

y=-(7/3)x+4/3

Reduce.

So we can see that the equation y=-(7/3)x+4/3

has a slope m=-7/3

and a y-intercept b=4/3

Now move onto the second equation.

-7y=1-3x

Subtract

from both sides.

-7y=-3x+1

Rearrange the terms.

y=(-3x+1)/(-7)

Divide both sides by

to isolate y.

y=((-3)/(-7))x+(1)/(-7)

Break up the fraction.

y=(3/7)x-1/7

Reduce.

So we can see that the equation y=(3/7)x-1/7

has a slope m=3/7

and a y-intercept b=-1/7

.

So the slope of the first line is m=-7/3

and the slope of the second line is m=3/7

.

Notice how the slope of the second line m=3/7

is simply the negative reciprocal of the slope of the first line m=-7/3

.

In other words, if you flip the fraction of the second slope and change its sign, you'll get the first slope. So this means that y=-(7/3)x+4/3

and

are perpendicular lines.

Question 175146This question is from textbook algebra 1
: the question says determine whether the graphs of the equations are parallel lines
1.x+4=y
y-x=-3
dANiELLE*This question is from textbook algebra 1
: the question says determine whether the graphs of the equations are parallel lines
1.x+4=y
y-x=-3
dANiELLE*
Answer by actuary(81)

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You can put this solution on YOUR website!
Rewrite both equations into slope intercept form.
1.x+4=y
y-x=-3
y=x+4 (line #1)
y=x-3 )line #2)
What is the slope of each line?
The slope of line 1 is 1
The slope of line 2 is 1.
Yes, the line are parallel.
Here is a graph of the two lines.
graph(300,300,-10,10,-10,10,x+4,x-3)

The lines differ because of different y-intercepts.
I hope that this helps.

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You can put this solution on YOUR website!
Solve both equations for

, in other words, perform whatever algebraic manipulations you need to have

on one side of the equal sign and everything else on the other side. Once you have done that, if the coefficient on the

in both equations is exactly the same, then the lines are parallel -- otherwise not.

Question 175130This question is from textbook
: select any two points on the line
(0,2)and(1,4)This question is from textbook
: select any two points on the line
(0,2)and(1,4)
Answer by stanbon(19714)

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select any two points on the line
(0,2)and(1,4)
------------------
slope = (4-2)/(1-0) = 2
intercept: (0,2)
----------
Equation:
y = 2x + 2
-----------
Points: (1,4); (3,8)
==========================
Cheers,
Stan H.

Question 175101This question is from textbook
: Write the point-slope form of the line that passes through (3,-3) and (5,1).This question is from textbook
: Write the point-slope form of the line that passes through (3,-3) and (5,1).
Answer by josmiceli(2170)

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You can put this solution on YOUR website!
(y - (-3)) / (x - 3) = (1 - (-3)) / (5 - 3)

answer

Question 175088This question is from textbook
: Find the slope of the line at passes through (3,6) and (1,-4).This question is from textbook
: Find the slope of the line at passes through (3,6) and (1,-4).
Answer by stanbon(19714)

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You can put this solution on YOUR website!
Find the slope of the line at passes through (3,6) and (1,-4).
----------------------
slope = (6--4)/(3-1) = 10/2 = 5
==================================
Cheers,
Stan H.

Question 175085This question is from textbook
: The profits made by Happenin'Hats depend on the number of hats they sell. If the company's weekly expenses are $2250 and they charge $45 per hat,their profits "p" can be calculated by the equation: p=45n-2250,where "n" is the number of hats sold. Write this relation in functional notation.This question is from textbook
: The profits made by Happenin'Hats depend on the number of hats they sell. If the company's weekly expenses are $2250 and they charge $45 per hat,their profits "p" can be calculated by the equation: p=45n-2250,where "n" is the number of hats sold. Write this relation in functional notation.
Answer by stanbon(19714)

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p(n) = 45n-2250
===================
Cheers,
Stan H.

Question 175077: Find the slope of the line that passes through the points (-3, -5) and (-5, 1).: Find the slope of the line that passes through the points (-3, -5) and (-5, 1).
Answer by Alan3354(1926)

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You can put this solution on YOUR website!
Find the slope of the line that passes through the points (-3, -5) and (-5, 1).
--------------
The slope, m, is the "rise over the run", the (diff in y)/(diff in x)
m = (-5-1)/(-3 - (-5))
m = -6/2
m = -3

Question 174911This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.
a.(h,0)
This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.
a.(h,0)

Answer by Mathtut(1331)

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You can put this solution on YOUR website!
if the equation is 2y=x+4 and y=0 then 2(0)=x+4
:
0=x+4
:
x=-4
:
therefore h=-4 since h=x and we have the ordered pair(-4,0)

Question 174912This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation .
b. (h,1)This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation .
b. (h,1)
Answer by mangopeeler07(448)

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You can put this solution on YOUR website!
y^2=x+4

.
(h,1)------------>this is in point form (x,y)

plug h in for x and 1 in for y:

1^2=h+4

Now simplify 1^2

Now subtract 4 from each side

-3=h

Question 174930This question is from textbook
: A teacher wises to schedule a quiz or exam during part of a two-hour class. The equation L+E=120 can be used to find the available lecture time "L" given that "E" minutes are planned for the quiz or exam. Determine the ordered pairs that satisfy the equation if the domain is {20,30,45,60}.This question is from textbook
: A teacher wises to schedule a quiz or exam during part of a two-hour class. The equation L+E=120 can be used to find the available lecture time "L" given that "E" minutes are planned for the quiz or exam. Determine the ordered pairs that satisfy the equation if the domain is {20,30,45,60}.
Answer by Mathtut(1331)

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You can put this solution on YOUR website!
Let E be the Domain{20,30,45,60} then the range is L
:
L=120-e
:
20: L=120-20=100
30: L=120-30=90
45: L=120-45=75
60: L=120-60=60
:
ordered pairs (20,100),(30,90),(45,75),(60,60)
:
If L is the Domain these ordered pairs would be reversed!!

Question 174913This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.
c. (h,2)This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.
c. (h,2)
Answer by Mathtut(1331)

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You can put this solution on YOUR website!
if the equation is 2y=x+4 and y=2 then 2(2)=x+4
:
4=x+4
:
x=0
:
therefore h=0 since h=x and we have the ordered pair(0,2)

Question 174931This question is from textbook
: Find given that This question is from textbook
: Find given that
Answer by Edwin McCravy(2190)

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You can put this solution on YOUR website!
Find matrix(1,3, 'g(',9,')')

given that matrix(1,5, 'g(',x,')','=',2x+3)


Substitute 9 for all the x's"



Simplify the right side:





Easy, wasn't it?

Edwin

Question 174932This question is from textbook
: Find given that This question is from textbook
: Find given that
Answer by Edwin McCravy(2190)

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You can put this solution on YOUR website!
Find matrix(1,3, 'h(',4,')')

given that matrix(1,5, 'h(',x,')','=',x/2-7)




Erase all the 's



Put 's where the 's were:



Simplify the right side:





Easy, wasn't it?

Edwin

Question 174933This question is from textbook
: Assume that y varies directly as x. Find y when x=54 if y=1/4 when x=3/2.This question is from textbook
: Assume that y varies directly as x. Find y when x=54 if y=1/4 when x=3/2.
Answer by stanbon(19714)

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You can put this solution on YOUR website!
Assume that y varies directly as x.
y = kx
---------
Find y when x=54
if y=1/4 when x=3/2.
(1/4) = k(3/2)
k = (2/3)(1/4) = 1/6
---
y = (1/6)54
y = 9
============
Cheers,
Stan H.

Question 174935This question is from textbook
: Assume that y varies inversely as x, and y=18 when x=3. Find the constant of variation.This question is from textbook
: Assume that y varies inversely as x, and y=18 when x=3. Find the constant of variation.
Answer by stanbon(19714)

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You can put this solution on YOUR website!
Assume that y varies inversely as x:
y = k/x
--------------------
y=18 when x=3
18 = k/3
--------------------
Find the constant of variation.
k = 3*18 = 54
===================
Cheers,
Stan H.

Question 174928: Is 2x+3y+7=3 a linear equation? If it is how do I write it in standard form?: Is 2x+3y+7=3 a linear equation? If it is how do I write it in standard form?
Answer by josmiceli(2170)

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You can put this solution on YOUR website!
Yes, if all the powers that the unknowns are raised to
are

, which they are:
2x^1 + 3y^1 + 7 = 3

then it is linear
The standard form is
ax + by + c = 0

Subtract

from both sides
2x + 3y + 4 = 0

Question 174907This question is from textbook algebra 1
: on a coordinate plane draw a verticle line that passes through (5,3)
This question is from textbook algebra 1
: on a coordinate plane draw a verticle line that passes through (5,3)

Answer by checkley75(3416)

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A verticle line has an undefined slope.
x=5 is the equation for this line.

Question 174905This question is from textbook algebra 1
: use the graphs of the equation y=x and y=100-x. These graphs intersect at one point. Explain why the point is not the intersection of the two graphs.
c.(1000,1000)This question is from textbook algebra 1
: use the graphs of the equation y=x and y=100-x. These graphs intersect at one point. Explain why the point is not the intersection of the two graphs.
c.(1000,1000)
Answer by josmiceli(2170)

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You can put this solution on YOUR website!
To be at the intersection, the given point would have to be
on both lines
y = x

It's on this line
y = 100 - x

not true, this point lies outside the line

Question 174915This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.
e. (h,-1)This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.
e. (h,-1)
Answer by Alan3354(1926)

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find the value of h such that the point satisfies the equation y2=x+4.
-------
What is "y2" ?

Question 174902This question is from textbook algebra 1
: use the graphs of the equation y=x and y=100-x. These graphs intersect at one point. Explain why the point is ot the intersection of the two graphs.
a.(100,25)This question is from textbook algebra 1
: use the graphs of the equation y=x and y=100-x. These graphs intersect at one point. Explain why the point is ot the intersection of the two graphs.
a.(100,25)
Answer by Alan3354(1926)

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use the graphs of the equation y=x and y=100-x. These graphs intersect at one point. Explain why the point is ot the intersection of the two graphs.
a.(100,25)
--------------
These 2 lines intersect at (50,50). All these other points are not (50,50).

Question 174916This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.
f. (h,-2)This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.
f. (h,-2)
Answer by nerdybill(1280)

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I'm assuming you mean:
y^2=x+4
.
Plugging in our values of (h,-2):
(-2)^2=h+4
4 = h+4
0 = h

Question 174916This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.
f. (h,-2)This question is from textbook algebra 1
: find the value of h such that the point satisfies the equation y2=x+4.