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How do you solve by graphing the following problems: y=2x and y=-2x + 8

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2 Answers

Hi Karen;
y=2x and y=-2x + 8
Both equations are in the format of...
y=mx+b
m is the slope.
b is the y-intercept, the value of y when x=0.
y=2x+0
slope is 2.
y-intercept is 0, corresponding to the point of (0,0).
Slope is change-of-y divided by change-of-x, also known as rise-over-run.  For this equation, you will begin with the provided point and move the line such that it rises 2 units, while running 1 unit to the right.  It will also descend 2 units, while running 1 unit to the left.
y=-2x + 8
slope is -2.
y-intercept is 8, (0,8).
For this equation, you will begin with the provided point and move the line such that it rises 2 units, while running 1 unit to the left.  It will also descend 2 units, while running 1 unit to the right.
You can check your work by verifying that the two lines met at the correct coordinate...
y=2x and y=-2x + 8
2x=-2x + 8
Let's add 2x to both sides of the equation...
2x+2x=2x-2x+8
4x=8
Divide both sides by 4...
(4x)/4=8/4
x=2
Plug this into one equation to establish the value of y.  The first equation is easiest...
y=2x
y=(2)(2)
y=4
Plug both results into the other equation to verify...
y=-2x + 8
4=[(-2)(2)]+8
4=-4+8
4=4
The two lines will meet at (2,4).
 
How do I solve the [system] by graphing?

y = 2x
y = -2x + 8

y = 2x is a line through the origin with slope 2.

y = -2x + 8 = -2(x - 4) is a line through (4,0) with slope -2.

Since the lines have opposite slopes they, along with the x-axis, will form an isosceles triangle having a vertex at x = (0+4)/2 = 2.

y = 2(2) = 4
y = -2(2)+8 = 4

Solution is (2,4).

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