Questions on Algebra: Coordinate systems, graph plotting, etc answered by real tutors!

Tutors Answer Your Questions about Coordinate-system (FREE)

Question 739009: graph the following system of equations using slope and y intercept determine the number of solutions for the system, 2x+3y=6 and 4x+6y=24
Answer by tommyt3rd(440)

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graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+-.67%2Ax%2B2%2C+-.67%2Ax%2B6+%29

these two lines clearly have the same slope yet they have different y-intercepts, so they must be parallel. Therefore the number of solutions is 0

Question 739295: Find the slope of a line perpendicular to each given line. y=-5/3x+3
Answer by tommyt3rd(440)

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the perpendicular slope is the negative reciprocal of the original so it is 3/5

:)

Question 728156: Write the equation in standard form of the circle with the given properties.
Center at the origin; r = square root of 7

Answer by tommyt3rd(440)

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origin => C(0,0) with r=sqrt%287%29

%0D%0A%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2%0D%0A

becomes

Question 748429: What linear equation represents a line containing the point (1,3)?
Answer by MathLover1(6618)

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y=mx

..........linear equation
if a line containing the point (

)

so, linear equation represents a line containing the point (

) is

Question 748408: What is the slope of the line that passes through the points (3,5) and (-2,2)?
Answer by rfer(12646)

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m=(2-5)/(-2-3)
m=-3/-5
m=3/5

Question 748386: A computer-aided design (CAD) operator has located three corners of a rectangle. The corners are at (8, 12), (-5, 12), and (-5, 6). Plot these points and find the location of the fourth corner.
I need help with this please
Answer by josgarithmetic(1476)

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Obviously the y coordinate of the unknown corner is 6. One of the sides is 13 units horizontally. From (-5,6) to (x, 6) to be 13 units, you must have x=8.

Question 748072: The distance between the two points A(a,1,2) and B(5,a,3) is 3. Find the value of .
Answer by tommyt3rd(440)

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If you mean find the value of a, then here we go:

It's convenient to use distance squared in this case (why?)

%0D%0A3%5E2=%285-a%29%5E2%2B%28a-1%29%5E2%2B%283-2%29%5E2%0D%0A

%0D%0A9=%2825-10a%2Ba%5E2%29%2B%28a%5E2-2a%2B1%29%2B%0D%0A1

and after some simplifying and rearranging
%0D%0A2a%5E2-12a-18=0%0D%0A

then

which is a perfect square and tells us a=3

Question 747424: Factor x3+1000:
Answer by lenny460(755)

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Factor: x^3 + 1000

We can solve the above using the sum of cubes formula:

Answer:
(x + 10)(x^2 - 10x + 100)

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 746036: i have tried but cant seem to figure it out !!p is the midpoint of line AB. what are the coordinates of point p? A(120) B(120)
Answer by Alan3354(30968)

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i have tried but cant seem to figure it out !!p is the midpoint of line AB. what are the coordinates of point p? A(120) B(120)
-----------------
A and B don't have (x,y) coordinates.
What does the (120) mean?

Question 745468: The ordinate of a point which is √29 units from (5,1) is twice its abscissa. Find the point.
Answer by sachi(392)

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as per question the point is (x,2x)
so the distance from (5,1)
is √[(x-5)^2+(2x-1)^2]=√29
or (x-5)^2+(2x-1)^=29
or x^2-10x+25+4x^2-4x+1=29
or 5x^2-15x-3=0
or 5x^2-15x-x-3=0
or (x-3)(5x+1)=0
or x=3 or -1/5
so y=6 or -2/5
so the points are (3,6) or (-1/5,-2/5)

Question 745466: Express by an algebraic equation the statement that the point (x,y) is at a distance 3 from (-7,-3)
Answer by stanbon(57224)

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Express by an algebraic equation the statement that the point (x,y) is at a distance 3 from (-7,-3)
-----
sqrt[(x+7)^2+(y+3)^2] = 3
==============================
Cheers,
Stan H.

Question 744087: I am using substitution to find coordinates for x and y. Problem reads: 2x+3y=25 , where y=3x+1.
I understood that to be 2x+3*(3x+1)=25,
Using distributive property, now I have 2x+9x+1=25.
Simplified that to 11x=24, or x=24/11
My textbook shows the correct final answer for coordinates is x=2, y=7, so I am way off. Can you tell where I went wrong?

Answer by stanbon(57224)

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I am using substitution to find coordinates for x and y.
Problem reads:
2x+3y=25
y = 3x+1
----------------------
I understood that to be 2x+3*(3x+1)=25,
Using distributive property, now I have 2x+9x+3 = 25.
Simplified that to 11x=22, or x = 2
Solve for "y":
y = 3x+1
y = 3*2+1 = 7
========================
My textbook shows the correct final answer for coordinates is x=2, y=7
========================
Cheers,
Stan H.

Question 742906: Plot the number 3/2 on a number line
Answer by rfer(12646)

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=+1.5

Question 742659: where would you plot y=x on a graph?
Answer by stanbon(57224)

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where would you plot y=x on a graph?
-----
Plot 2 points:
Let x = 1, then y = 1 giving you point (1,1)
-----
Let x = 3, then y = 3 giving you point (3,3)
=============
Cheers,
Stan H.
=============

Question 742331: .)Given the equation of a basic graph and describe a sequence of transformation that can be used to find the graph of y=-|2x-3| DONOT GRAPH .
Basic graph equation:__________
Transformations:

10.)Calculate an equation for the circle for which the segment represent PQ is a diameter
P=(-3,1) , Q=(5,6)

Answer by stanbon(57224)

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Given the equation of a basic graph and describe a sequence of transformation that can be used to find the graph of y=-|2x-3| DONOT GRAPH .
Basic graph equation: y = |x|
Transformations:
1st: horizontal stretch by factor of 2
2nd: shift 3 units to the right
3rd: reflect in the x-axis
=====================================
10.)Calculate an equation for the circle for which the segment represent PQ is a diameter
P=(-3,1) , Q=(5,6)
-----
Find Center (x,y)
x = (-3+5)/2 = 1
y = (6+1)/2 = 3.5
---------------------
Find the Radius:
r = sqrt[(-3-1)^2 + (1-3.5)^2] = sqrt[16+6.25] = sqrt(22.25)
------
Equation:
(x+3)^2 + (Y-1)^2 = 22.25
=============================
Cheers,
Stan H.

Question 742329: Help!
6.)find the function that is finally graphed after the following transformations in indicated order are applies to the graph of y=|x|
1.) Right shift by 4 units
2.) Reflection with respect to the x-axis
3.) Horizontal stretch by a factor of 2
4.) Shift downwards by 2 units

Answer by stanbon(57224)

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6.)find the function that is finally graphed after the following transformations in indicated order are applies to the graph of
y=|x|
1.) Right shift by 4 units
y = |x-4|
----------
2.) Reflection with respect to the x-axis
y = -|x-4|
---------------
3.) Horizontal stretch by a factor of 2
y = -2|x-4|
-----------------------
4.) Shift downwards by 2 units
y = -2|x-4|-2
=================
Cheers,
Stan H.
=================

Question 742325: Can someone assist me??please.
i)state the transformations applied to the graph of f(x)=|x| to obtain the graph of g(x)=-2|x-3|+1
ii)Sketch the graph.Show and label at least 3 points of transformations used to draw your graph.

Answer by stanbon(57224)

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Can someone assist me??please.
i)state the transformations applied to the graph of f(x)=|x| to obtain the graph of g(x)=-2|x-3|+1
-----
1st: shift 3 to the right
2nd: reflect in the x-axis
3rd: stretch by a factor of 2
4th: vertical transformation of +1
-----------------------------------------------
ii)Sketch the graph.Show and label at least 3 points of transformations used to draw your graph.
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-2%2Aabs%28x-3%29%2B1%29

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-2%2Aabs%28x-3%29%2B1%29

--------------------------------------------------
Cheers,
Stan H.

Question 740984: PLEASE HELP ME SOLVE THIS!!!
Point "A" (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point "B" so that the line x = 2 is the perpendicular bisector of "AB", with a line drawn above "AB"?
Answer by ankor@dixie-net.com(15628)

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Point "A" (-4,1) is in the standard (x,y) coordinate plane.
What must be the coordinates of point "B" so that the line x = 2 is the perpendicular bisector of "AB", with a line drawn above "AB"?
;
Since the bisector is a vertical line, line AB is a horizontal line.
:
The best way to understand this is use graph paper. Draw the x/y, point -4,1;
the line for x=2 is a vertical line going thru x=2, will cross Line AB at x/y point 2,1
As you can see, Line AB will between points -4,1 and 8,1

Question 740020: Find the circumference of each circle. Use 3.14 for Pie. Round to the nearest tenth
10 in.
Answer by Alan3354(30968)

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Find the circumference of each circle. Use 3.14 for Pie. Round to the nearest tenth
10 in.
------------
You didn't say what the 10 inches is.
If it's radius,
C = 2*pi*r
--------------
PS It's the Greek letter pi, not the dessert pie.

Question 739893: find the slope of the line passing through the given points (-1/3, 1/5) and (3/2, 1/4)
Answer by Alan3354(30968)

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find the slope of the line passing through the given points
(-1/3, 1/5) and (3/2, 1/4)
------------
m = diffy/diffx = (1/20)/(11/6)
m = 3/110

Question 25265: USE THE GRAPHING METHOD TO TELL HOW MANY SOLUTIONS THE SYSTEM HAS:
x+y=8
x+y=-1
Answer by jam123(17)

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x+y = 8, so
y = 8-x
x+y=-1 so
y=-1-x
+graph%28+700%2C+700%2C+-5%2C+5%2C+-5%2C+5%2C+8-x%2C+-1-x%29+

The lines are parallel so there are no solutions.

Question 739518: HOW DO YOU FIND ORDERED PAIRS IF YOU DO NOW KNOW THE EQUATION

Answer by AnlytcPhil(1276)

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If you will, in the thank-you note space, state the 
problem and instructions exactly word-for-word as it 
is stated in your book, I will answer it.

Phil

Question 739298: Find the slope of a line perpendicular to each given line. y=2/3x+4
Answer by Alan3354(30968)

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Find the slope of a line perpendicular to each given line. y=2/3x+4
==========================
Slope of the given line is 2/3
Slope of lines perpendicular is the negative inverse of 2/3.

Question 739059: find the value of the missing coordinate in (x,5)that makes the orderd pair a solution to the equation 2x+y=-1
Answer by opie95(4)

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put your y coordinate in and solve the equation
2x+5=-1
2x=-6
x=-3
subtract 5 from both sides which gives you -6
divide both sides by 2
x=-3

Question 739025: find the slope of a line parallel to each given line. y=2
Answer by reviewermath(500)

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y = 2 is a horizontal line, therefore the slope of any line
parallel to it is highlight%280%29

(zero).

Question 739021: Can you please help me. I need to find the slope of a line parallel to each given line. y=3/4x
Answer by rfer(12646)

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parallel slope is still 3/4

Question 738551: Can you please help me find the slope of a line perpendicular to each given line. y=-5/3x+3
Answer by MathLover1(6618)

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given line: y=-%285%2F3%29x%2B3

...compared to slope-intercept

form

, you see that slope m=-%285%2F3%29

the slope of a line perpendicular to given line will have a slope m%5Bp%5D=-1%2Fm

so, a slope is m%5Bp%5D=%28%28-1%29%2F%28-5%2F3%29%29

Question 738549: please help me find the slope of a line parallel to each given line. y=-2x+1
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(6618)   (Show Source):
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you are given a line , and it is already in form where and
so, the slope of given line is
by definition, a line parallel to given line has same slope; so,

Answer by jim_thompson5910(28476)   (Show Source):
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The slope of this line is -2

The slope of ANY line parallel to this one will also be -2 since all parallel lines have the same slope

So the answer is -2

Question 738547: Can you please help me find the slope of a line perpendicular to each given line. y=1/2x-5
Answer by jim_thompson5910(28476)   (Show Source):
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The slope of this given line is 1/2

Flip the fraction to get 2/1 = 2

Flip the sign to get -2, this is the perpendicular slope. A good way to remember finding it is: Start with the given slope, turn it into a fraction (if necessary), then flip the fraction and flip the sign to get the perpendicular slope.

So the answer is -2

Question 738360: Can you please help me find the slope of the line parallel to each given line.
y=-x-1
Answer by jim_thompson5910(28476)   (Show Source):
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y = -x-1 is the same as y = -1x-1 which is in the form y = mx+b

So the slope is m = -1

All lines parallel to this one will also have a slope of -1 since parallel lines have equal slopes

So the final answer is -1

Question 738359: Can you please help me find the slope of the line parallel to each given line.
y=x-1
Answer by jim_thompson5910(28476)   (Show Source):
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y = x - 1 has a slope of 1 since it's in the form y = mx+b where m = 1

ANY line parallel to this one will also have a slope of 1 because any two parallel lines have the same slope.

So the answer is 1

Question 738262: Can you please help me find the slope of the line through each pair of points.
(-6,2),(7,2)
Answer by richwmiller(9135)   (Show Source):
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y=2 is the line
since y doesn't change the slope is zero

Question 738201: What are the coordinates of the point 3 units from the y-axis at a distance √5 from (5,3)?
Answer by josgarithmetic(1476)   (Show Source):
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This would be difficult to use the system to show a drawing and graph, but I am handling it like:

The line x=3, y=infinity,
A segment with endpoint at (5,3) and perpendicular to the line x=3, will be seen to intersect the line x=3 AT the point (3, 3).
EITHER of two points are also on the line x=3, and each of these is from the point (5, 3), but we do not yet know the y coordinate for this point.
... BUT we DO have a triangle, actually a RIGHT triangle and we can find the length up or down from point (3, 3) using pythagorean theorem.

From (3, 3) to (5, 3) is 2 units.
From (5, 3) to (3, u) is units.
From (3, u) to (3, 3) is h
Let's find h using pythagorean theorem.

Therefore, u=3-1, .
ANSWER: The coordinate pair for the specified point is then either (3, 2) or (3, 4).

Question 738113: can you please help me find the slope of the line (7,14),(16,-8). I came up with -9/22
Answer by DrBeeee(376)   (Show Source):
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Your answer is upside down. The slope is
(1) m = (y1-y2)/(x1-x2) or
(2) m = (14-(-8))/(7-16) or
(3) m = 22/(-9) or
(4) m = -22/9

Question 738040: I need help finding the slope of the line through each pair of points.
(19,11),(20,13).. I came up with 1/2

Answer by rfer(12646)   (Show Source):
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m=(13-11)/(20-19)
m=2/1
m=2

Question 737672: I need to find the slope. (19,-6),(-15,9). Thank you!
Answer by reviewermath(500)   (Show Source):
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The slope is equal to

Question 736662: I am confused on this problem.
Find the equation for the circle with a diameter whose endpoints are (-3,-5)(-5,4).
Answer by lynnlo(4155)   (Show Source):
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(x+4)^2+(y+1/2)^2

Question 736571: i need help with graphing -2x-y=-2

Answer by stanbon(57224)   (Show Source):
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i need help with graphing -2x-y=-2
---------
Solve for "y":
y = -2x+2
-----
Plot 2 points:
(0,2) and (1,0)
-------
Draw a line thru those two points:

------------
Cheers,
Stan H.
==========

Question 736459: I am so lost can you please help? I need to solve and graph y=-x
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(9654)   (Show Source):
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Make a chart that has columns labeled and
Under the column, you will pick values that are
pretty close to , like:
-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
( remember: write these vertically )
Now alongside each of these values for , you will fill in a
value for

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

-----------
etc.
When you get to ,

-----------

----------

----------
etc.
After you have filled the chart, each pair of ( x,y )
entries is a point that you will plot, so you
have the points:
( -10, 10 )
( -9, 9 ),
( -8, 8 ),
etc.
For plotting, the origin is (0,0) and positive x is to the right,
negative x is to the left, positive y is up, and
negative y is down.
You will end up with the following plot:

You can plot any equation with this method

Answer by Alan3354(30968)   (Show Source):
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Same as this one:
------------
solve and graph y=x-2
================
It is solved for y.
You can solve for x: x = y+2
--------------
It's 1 equation in 2 variables, --> an infinite # of solutions.
y = x-2
You can pick any number for x and find y.
----
To graph it, you need 2 points.
Pick 2 values for x and find y.
x = 0, y = -2 --> point (0,-2)
x = 2, y = 0 --> point (2,0)
x = 100, y = 98 --> (100,98)
------
Plot at least 2 points, draw a line thru them.
Every point on the line is a "solution."

Question 736458: Can you please help me solve and graph y=x-2? It has been a very long time since I have done this and I am lost.
Answer by Alan3354(30968)   (Show Source):
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solve and graph y=x-2
================
It is solved for y.
You can solve for x: x = y+2
--------------
It's 1 equation in 2 variables, --> an infinite # of solutions.
y = x-2
You can pick any number for x and find y.
----
To graph it, you need 2 points.
Pick 2 values for x and find y.
x = 0, y = -2 --> point (0,-2)
x = 2, y = 0 --> point (2,0)
x = 100, y = 98 --> (100,98)
------
Plot at least 2 points, draw a line thru them.
Every point on the line is a "solution."

Question 736303: what is or how do you simplify this expression -7(2v+6)-2
Answer by lynnlo(4155)   (Show Source):
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PROBLEM:
-7(2V+6)-2
EXPAND "-7"BY USING ASSOCIATIVE PROPERTY ON(2V+6)
-7(2V-7)6-2
MULTIPLY INTEGERS
-14V-7(6-2)
MULTIPLY INTEGERS
-14V-42-2
ADD INTEGERS TOGETHER
-14V+-44
REMOVE (+)IN FRONT OF "-44"
ANSWER======-14V-44

Question 734960: Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. (-8,3) y+4=-(2/3)(x-2)
Answer by josgarithmetic(1476)   (Show Source):
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Interesting that you showed your given line in almost correctly point-slope form as plain text. Your post is now edited for this correction to eliminate possible confusion, ------

The slope that you will want is the negative reciprocal of , which will be . You now expect an equation for your desired line to be , where the point (u, v) is any point which you want your line to contain. The given point for (u, v) is (-8, 3), so just substitute those values:

and the rest to be done is a couple steps of arithmetic.

Question 734984: Two lines in a coordinate plane have no points of intersection. Which of these could be the equations of the lines?
A. 4x+2y=6 C.4x+=6
10x+5y=7 5x-10y=6
B. 4x+2y=6 D. 5x+10y=6
10x+5y=15 5x-10y=6
Answer by lynnlo(4155)   (Show Source):
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B.