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On a city delivery map drawn on a coordinate grid, a courier's route runs in a straight line. The route passes through the depot at the point (2, 9) and through a checkpoint at the point (6, 3). At what y-coordinate does the route cross the vertical street x = 12?
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Correct answer
B
Find the slope from the two given points, then extend the line to x = 12. Slope m = (3 − 9)/(6 − 2) = −6/4 = −3/2 (the route falls 3 units for every 2 units to the right). Using the depot (2, 9): y = 9 + (−3/2)(12 − 2) = 9 + (−3/2)(10) = 9 − 15 = −6.
Check from the checkpoint (6, 3): y = 3 + (−3/2)(12 − 6) = 3 − 9 = −6, which agrees. So the route crosses x = 12 at y = −6, choice B.
Why the others tempt: A, −15, comes from using 12, the bare x-coordinate, as the run from the checkpoint instead of the displacement 6, a wrong-distance slip. C, −1, comes from flipping the slope to −2/3, the change in x over the change in y, the classic slope-inversion error, then running 6 from the checkpoint. D, 3, comes from simply keeping the checkpoint's y-value, treating the line as flat beyond the checkpoint and never applying the slope. E, 6, has the right size but the wrong sign: the line keeps descending below the x-axis, so the crossing is at −6, not +6.
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