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?
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.