the slope of the line through (1,2) and (x,0) is the negative of the slope through (4,5) and (x,0). find x

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For this problem, you can set up the slope for both lines, and set one equal to the negative of the other.

slope 1 = (0-2) / (x-1) = -2 / (x-1)

slope 2 = (0-5) / (x-4) = -5 / (x-4)

Now set slope 1 = -slope 2

-2/(x-1)=5/(x-4)

Now cross multiply the proportions.

-2(x-4) = 5(x-1)

Distribute and simplify.

-2x+8 = 5x-5

13=7x

x=13/7

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