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

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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).

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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