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

You can put this solution on YOUR website!
How do I write an equation in slope intercept form for the line that passes through (5,6) and is parallel to the line described by 4x - 5y = 20
.
First, determine slope of
4x - 5y = 20
.
do this by putting it into slope-intercept form y=mx+b:
4x - 5y = 20
-5y = -4x + 20
5y = 4x - 20
y = (4/5)x - 16
slope is 4/5
since the new line is parallel it must have the same slope.
.
Plug the slope (4/5) and the given point (5,6) into the point-slope form:
y - y1 = m(x - x1)
y - 6 = (4/5)(x - 5)
y - 6 = (4/5)x - 4
y = (4/5)x - 4 + 6
y = (4/5)x + 2 (this is what they're looking for)

You can put this solution on YOUR website!
year Record time
1920 45.4 seconds
1970 44.4 seconds
Difference
50 -1
rate of reduction per year =-1 /50 = -0.02

R(t)= 45.4-0.020t

2003 t=83

R(t)= 45.4 + -0.020 * 83

R (83)= 43.74 seconds
------------

R(t)= 45.4-0.02t
43.5=45.4-0.02t
45.4-43.5=0.02t
1.9=0.02t
t= 1.9/0.02
t=95 years
1920 +95 = 2015
year 2015 it will bve 43.5 seconds

You can put this solution on YOUR website!
4y=3(y+2)
4y=3y+6
4y-3y=6
y=6
y=(0)x+6
Compare above equation with standard equation of the line
y=mx+b
Slope = m = 0, y-intercept = b = 6
Slope of the line is zero, it is a horizontal line.

You can put this solution on YOUR website!
Find the line containing P(3,0) and perpendicular to the x-axis.
x=3
Find the line containing P(-4,5) and parallel to x-axis.
y=5

You can put this solution on YOUR website!
x-2y = 4
Find the slope of this line

-2y=-x+ 4
Divide by -2
y = 1/ 2 x-2
Compare this equation with y=mx+b
slope m = 1/ 2

The slope of a line perpendicular to the above line will be the negative reciprocal -2
m1*m2=-1


m= -2 ,point ( -2 , -4 )
Find b by plugging the values of m & the point in
y=mx+b
-4=4+b
b= -8
m= -2
The required equation is y=-2x-8
m.ananth@hotmail.ca

You can put this solution on YOUR website!
What is the slope of
3x=4y-2
Add 2 to both sides to solve for "y":
4y = 3x+2
Divide both sides by 4 to get:
y = (3/4)x + (1/2)
----
slope = 3/4
==================
cheers,
Stan H.

You can put this solution on YOUR website!
uh i think u forgot to add the question?

You can put this solution on YOUR website!
um...if its y=-2/5 or y=4/5 there is still no slope so the answer would be 0

You can put this solution on YOUR website!
Find an equation of the line containing the given pair of points.
(1/4, -1/2) and (3/4, 6)
x1 y1 x2 y2
1/ 4 1/ 2 3/ 4 6

slope m = (y2-y1)/(x2-x1)
( 6 - 1/2 )/( 3/4 - 1/4 )
( 5.5 / 0.5 )
m= 11

Plug value of the slope and point ( 1/4 , 1/2 ) in
Y = m x + b
1/2 = 11/4 + b
b= 0.5 - 11/4
b= -9/ 4
So the equation will be
Y = 11 x -9/4
What is the equation of the line? y=
second question
Find an equation of the line having the given slope and containing the given point.
m=6/7, (1, -7)
m= 6/ 7

Plug value of the slope and point ( 1, -7
Y = m x + b
-7.00 = 6/7 + b
b= -7 - 6/7
b= -55/ 7
So the equation will be
Y = 6/7 x -55/7
The equation of the line is Y=
Third question
Find an equation of the line containing the given pair of points.
(-1, -2) and (-4, -6)
x1 y1 x2 y2
-1 -2 -4 -6

slope m = (y2-y1)/(x2-x1)
( -6 - -2 )/( -4 - -1
( -4 / -3 )
m= 4/ 3

Plug value of the slope and point ( -1 , -2 ) in
Y = m x + b
-2.00 = -4/3 + b
b= -2 - -4/3
b= - 2/ 3
So the equation will be
Y = 4/3 x - 2/3
The equation of the line in slope-intercept from is y=
Fourth Question
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b
(-4, 7); 4x=3y+2
4 x + -3 y = 2
Find the slope of this line
make y the subject
-3 y = -4 x + 2
Divide by -3
y = 4/ 3 x - 2/3
Compare this equation with y=mx+b
slope m = 4/3
The slope of a line parallel to the above line will be the same
The slope of the required line will be 4/3
m= 4/3 ,point ( -4 , 7 )
Find b by plugging the values of m & the point in
y=mx+b
7 = -16/3 + b
b= 37/3
m= 4/3
Plug value of the slope and b in y = mx +b
The required equation is y = 4/3 x + 37/3


The equation of the line is y=
Fifth question
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b
(5, 7); 5x+y=4
5 x + 1 y = 4x+5y=2
Find the slope of this line
make y the subject
1 y = -5 x + 4
Divide by 1
y = -5 x + 4
Compare this equation with y=mx+b
slope m = -5
The slope of a line parallel to the above line will be the same
The slope of the required line will be -5
m= -5 ,point ( 5 , 7 )
Find b by plugging the values of m & the point in
y=mx+b
7 = -25.00 + b
b= 32
m= -5
Plug value of the slope and b in y = mx +b
The required equation is y = -5 x + 32
the equation of the line is y=
Sixth question
Write an equation of the line containing the given point and perpendicular to the given line.
(5, -4); 4x+3y=8
4 x + 3 y = 8
Find the slope of this line

3 y = -4 x + 8
Divide by 3
y = -1 1/ 3 x + 2.67
Compare this equation with y=mx+b
slope m = -4/ 3

The slope of a line perpendicular to the above line will be the negative reciprocal 3/4
m1*m2=-1


m= 3/4 ,point ( 5 , -4 )
Find b by plugging the values of m & the point in
y=mx+b
-4 = 15/4 + b
b= -31/4
m= 3/4
The required equation is y = 3/ 4 x -31/ 4

The equation of the line is y=
m.ananth@hotmail.ca

You can put this solution on YOUR website!
1 y = 5 x -3
Divide by 1
y = 5 x -3
Compare this equation with y=mx+b
slope m = 5

The slope of a line perpendicular to the above line will be the negative reciprocal - 1/5
m1*m2=-1


m= - 1/5 ,point ( 2 , 1 )
Find b by plugging the values of m & the point in
y=mx+b
1 = -2/5 + b
b= 7/5
m= - 1/5
The required equation is y = - 1/ 5 x + 7/ 5
m.ananth@hotmail.ca

You can put this solution on YOUR website!
1 x + 7 y = 3
Find the slope of this line
make y the subject
7 y = -1 x + 3
Divide by 7
y = - 1/ 7 x + 3/7
Compare this equation with y=mx+b
slope m = - 1/7
The slope of a line parallel to the above line will be the same
The slope of the required line will be - 1/7
m= - 1/7 ,point ( 3 , 6 )
Find b by plugging the values of m & the point in
y=mx+b
6 = -3/7 + b
b= 45/7
m= - 1/7
Plug value of the slope and b in y = mx +b
The required equation is y = - 1/7 x + 45/7

m.ananth@hotmail.ca

You can put this solution on YOUR website!
x=3 3/7

You can put this solution on YOUR website!
Polynomials are defined everywhere, so the domain of P is (-infinity, infinity).

You can put this solution on YOUR website!
Because it makes solving them easier, that's the main reason. For example,



Clear fractions by cross-multiplying to get



Same reasoning applies to decimals.

You can put this solution on YOUR website!
No, if you rearrange and put in y = mx + b form, you will see that the slopes are the same, and that the graphs of the two lines are parallel.

You can put this solution on YOUR website!
1. 4x-16y=2
16y=4x-2
/16
y=(1/4)x-(1/8)
slope of this line is (1/4)
The parallel line will have same slope = 1/4
point = (-2,-6)
Find b , plug point and slope in the equation y = mx+b
-6=(1/4)(-2)+b
-6=(-1/2)+b
-6+1/2=b
b=-5 1/2
b= -11/2
Equation ; y= (1/4)x-11/2
---
4 x -16 y = 2
Find the slope of this line

-16 y = -4 x + 2
Divide by -16
y = 0.250 x + -0.13
Compare this equation with y=mx+b
slope m = 1/4

The slope of a line perpendicular to the above line will be the negative reciprocal -4
m1*m2=-1
The slope of the required line will be -4
m= -4 ,point ( -2 , -6 )
Find b by plugging the values of m & the point in
y=mx+b
-6 = 8 + b
b= -14
m= -4
The required equation is y =-4x-14
m.ananth@hotmail.ca

You can put this solution on YOUR website!
Pleas help me solve this equation:
If y= -4 when x = 10, find y when x = 5
--------------
Not enough info
What's the relation between x & y?

You can put this solution on YOUR website!


Multiply the first equation by 2, then multiply the second equation by 9:





Note that the coefficients on in the two equations are now additive inverses. Add the two equations to each other then solve the resulting single variable equation for . Once you have determined the value for , substitute that value back into either original equation and solve for

John

My calculator said it, I believe it, that settles it

You can put this solution on YOUR website!
Solve for x to get x = -2, and because there are no y terms, this means that the slope is undefined.

You can put this solution on YOUR website!
28-4y=0
adding 4y to both sides:
28 = 4y
dividing both sides by 4:
7 = y

You can put this solution on YOUR website!
I think you means,"solve this using the elimination method"
:
2 - 7x = 9y
2y -4x = 6
:
Put both equations into standard form
-7x - 9y = -2
7x + 9y = 2; multiplied by -1:
and
2y - 4x = 6
-4x + 2y = 6
:
multiply the 1st equation by 4, and the 2nd equation by 7, results
+28x + 36y = 8
-28x + 14y = 42
-----------------addition eliminates x, find y
0x + 50y = 50
y = 50/50
y = 1
:
Use the 1st original equation to find x, 2 - 7x = 9y
replace y with 1
2 - 7x = 9(1)
-7x = 9 - 2
-7x = 7
x =
x = -1
:
The solutions: x=-1, y=1
:
You can check this in the 2nd original equation
:

You can put this solution on YOUR website!
solve for y

the general slope-intercept equation is ___ y = mx + b, where m is the slope and b is the y-intercept

You can put this solution on YOUR website!
y=5
if its parallel to x axis its a horizontal line

You can put this solution on YOUR website!
ADD 6X to both sides
ADD 9 to both sides
DIVIDE by 7

You can put this solution on YOUR website!
Write a rule for the linear function whoes graph has slope m and contains the given point. m=3; (-2,2)
:
Using the format: mx + b = y
:
replace m and y to find b
:
3(-2) + b = 2
-6 + b = 2
b = 2 + 6
b = 8
:
The equation: y = 3x + 8

You can put this solution on YOUR website!
Write the slope-intercept equation for the
line that passes through (-4, 6) and (2, -6).
-------
slope = (-6-6)/(2--4) = -12/6 = -2
----
Form: y = mx + b
6 = -2(-4) + b
6 = 8 + b
b = -2
---------
Equation:
y = -2x - 2
================
Cheers,
Stan H.
================

You can put this solution on YOUR website!
A linear equation in two variables is an equation with two variables (usually called x and y) where the variables are at most multiplied by a number, and added to something else. No exponents, no variables in denominators, no fancy functions of the variables.
For example 2x-y=3 and x+y=3 are linear equations.
A set of linear equations is a system of linear equations. A typical set of linear equations in two variables is:
2x-y=3
x+y=3
As the name hints, a linear equation in two variables gives you a straight line when you plot points for data pairs (x,y) that satisfy the equation. With two of those linear equations, you could expect to get two straight lines. Their intersection would represent the solution to the system of equations.
The graph for the two equations could be the same line (if the equations are equivalent to each other, like x+y=3 and 2x+2y=6). Then you would have infinite solutions, represented by all the points in the common line.
You could also end up with two parallel lines, that have no point in common, and the system would have no solution.
In the case of 2x-y=3 and x+y=3, the straight lines representing those equations cross at a point that belongs to both lines. That point represents the solution to the system made of those two equations. The point (2,1), with x=2 and y=1, is the intersection of the graphs for the equations above and the solution of the system of equations. The set of variable values x=2 and y=1 satisfies both equations.
How to graph linear equations and how to solve a system of linear equations could be your next questions. I am just glad that I do not have to answer them, at least for now.

You can put this solution on YOUR website!
word problem: cd case=$35, cds=$20each. Write the linear function for finding the cost, c, of buying a cd case and d cds. I have c=20d + 35.
---
That looks good.

You can put this solution on YOUR website!
solve the system by graphing 2x+y=-7 & 5x+4y=-13. I How do I solve the problems to get the solutions to graph.
--------------
You don't "get the solution to graph."
You graph the 2 equations. Each is a straight line. Every point on the line is a solution to that equation.
---
Where they intersect, the point that's on both equations, is the solution to the system of equations.
-----------
2x+y=-7
y = -2x - 7
You need 2 points for a straight line.
Pick 2 values for x and find y.
Plot the 2 points.
Draw a line thru them.
====================
Do the same for the other equation.

You can put this solution on YOUR website!
is a horizontal line through the point (0,2)
The slope is ( change in y ) / ( change in x )
The change in y is always zero, so slope =
Any line perpendicular has slope = ,
which is infinite.

You can put this solution on YOUR website!
The letter m is often used for slope of a line, and that’s what I bet the M in your problem stands for.
The slope of the line connecting ( n , 11/2 ) and ( - 1/4 , 0 ) is the difference in y-coordinates divided by the difference in their x-coordinates:
Slope=m=
--> --> --> -->
The slope of the line connecting ( 4 , n ) and ( 1 , a-b) is
Slope=
--> -->

You can put this solution on YOUR website!
Use the point-slope formula


Multiply both sides by




or, in standard form:

You can put this solution on YOUR website!

You can put this solution on YOUR website!
x/5+9=4

x/5+9-9=4-9

x/5 = -5

x = -5*5

x = -25

So the solution is x = -25

-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

You can put this solution on YOUR website!
Write the equation of a line parallel to and passing through (2,1).
---------
Parallel to what?

You can put this solution on YOUR website!
x - y = 3
subtract x from both sides of the equation to get:
-y = -x + 3
multiply both sides of the equation by -1 to get:
y = x - 3

that's one way.
here's another way.

x - y = 3
add y to both sides of the equation to get:
x = y + 3
subtract 3 from both sides of the equation to get:
x - 3 = y
by the laws of commutation, if a = b then b = a which allows you to make the equation be equal to:
y = x - 3

You can put this solution on YOUR website!
A company predicts that it will sell y units of its product if it charges x dollars for it using the formula y=300-2.5x. In whole dollars, how much should the company charge for the product if it wants to sell 175 units.
**
This equation is for a straight line of the standard form: y=mx+b, m=slope, b=y-intercept
175=300-2.5x
y=-2.5x+300
175=-2.5x+300
2.5x=300-175
2.5x=125
x=125/2.5=50
ans:
The company charge for the product should be $50

You can put this solution on YOUR website!
3x - 8y = -6
32x + 12y = -6
Write the equations in slope intercept form

8y=3x+6
/8
y=(3/8)x+6/8
y=(3/8)x+3/4...........................(1)

32x + 12y = -6
12y=-32x-6
/12
y=-4x-(1/2).............................(2)
compare these equations with y= mx+b where m is the slope
slope of first line is(3/8) & second line is(-4)
the slopes of both these equations are are neither the same nor the negative reciprocal of each other.
So they are neither parallel nor perpendicular.

You can put this solution on YOUR website!
4 x + 5 y = 20
Find the slope of this line
make y the subject ( rewrite in slope intercept form)
5y=-4x+20
Divide by 5
y =- ( 4/ 5)x+4
Compare this equation with y=mx+b
slope m = - 4/ 5
The slope of a line parallel to the above line will be the same
The slope of the required line will be- 4/ 5
m= - 4/ 5 ,point ( 2 , 1 )
Find b by plugging the values of m & the point in y=mx+b
1=-4/5 * 2+b
1 +8/ 5 = b
b= 13/ 5
m= - 4/5
Plug value of the slope and b in y = mx +b
The required equation is y = - 4/5 x + 13/5

m.ananth@hotmail.ca

You can put this solution on YOUR website!
3x - 2y = 1

- 2y = -3x + 1

y = 3/2x - 1/2


So the answer is choice C
-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

You can put this solution on YOUR website!
is the equation of a line in slope-intercept form
That form starts with "y=", has the y-intercept for a constant/independent term, and has the slope for coefficient of the . The slope is in this case.

Solving for , we get the slope intercept form
--> --> --> --> -->
The slope is
I suspect a typo, but if it was really written like that, it is really
--> --> -->
Without doing that division we see that is constant, while could be anything. There is no slope. The slope is undefined, and the line is a vertical line.
is the equation in point-slope form of the line with slope that passes through the point (4,3).
is the equation in point-slope form of the line with slope that passes through the point (4.0856,7.3591).

You can put this solution on YOUR website!
slope = ( change in y ) / ( change in x )
( 5/6, -2 ) and ( -1/3, -1/3 )
slope =
-----------------------

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

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

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

You can put this solution on YOUR website!


By substitution. You have two expressions in both equal to . Set them equal to each other and then solve for . Once you have the value of that satisfies both equations at the same time, plug in the value to either equation and solve for

John

My calculator said it, I believe it, that settles it