In the x-y plane, the x-axis and the graphs of the lines y = x, y = 1, and y+x=4 intersect to form a trapezoid. What is the sum of the slopes of the two nonparallel sides of the trapezoid?

A) -2

B) -1

C) 0

D) 1

E) 2

OK, so the *x*-axis and the *y* = 1 line are parallel—those are both horizontal lines. So we don’t care about those. We only care about the nonparallel lines, which are *y* = *x* and *y* + *x* = 4.

*y* = *x* has a slope of 1–that’s easy. To find the slope of the other line, put it in slope-intercept form:

*y* + *x* = 4

*y* = –*x *+ 4

That’s got a slope of –1. Therefore, the sum of the slopes of the nonparallel lines is 1 + (–1) = 0.

## Comments (1)

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