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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 (change in x over 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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