What is the y-coordinate of the y-intercept of the line representing the second corridor?

Question

An urban beekeeping cooperative maps rooftop apiaries in the xy-plane, where each unit represents 100 meters. A pollination corridor is represented by the line that passes through the apiaries at (-5, 12) and (7, 3). A second corridor is represented by a line that is parallel to the first corridor and passes through the apiary at (3, -2).

Accepted Answer

C. 1/4. The first corridor has slope (3 - 12)/(7 - (-5)) = -9/12 = -3/4, and a parallel line has the same slope. Using (3, -2): -2 = (-3/4)(3) + b, so b = -2 + 9/4 = 1/4. Choice B comes from computing the slope as 3/4 (subtracting the coordinates in inconsistent orders or dropping the negative sign). Choice D comes from using the reciprocal slope -4/3. Choice A comes from using 4/3, the perpendicular slope, instead of the parallel slope.

Answer

A. -6 — You used 4/3, the perpendicular slope, but the second corridor is parallel, so it keeps the slope -3/4. That gives b = 1/4.

Answer

B. -17/4 — You computed the slope as 3/4 instead of -3/4 — the rise is 3 - 12 = -9, so the slope is -9/12 = -3/4, and b = 1/4.

Answer

D. 2 — You flipped the slope to -4/3 instead of keeping -3/4. Parallel lines have identical slopes, not reciprocal ones, so b = -2 + 9/4 = 1/4.

Algebra practice question

Answer: C. 1/4

Why the other answers are wrong

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