SAT Math Multiple Choice Practice Question 148: Answer and Explanation

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Question: 148

16. Line l passes through the origin and has a slope of 2/3. Line m is perpendicular to line l and intersects it at the point (-6, -4). Where does line m cross the y-axis?

A. (0, -18)
B. (0, -13)
C. (0, -8)
D. (0, 5)
E. (-82/3, 0)

Correct Answer: B

Explanation:

B. Perpendicular lines have slopes that are negative reciprocals, so line m has a slope of -3/2. Because m passes through (-6, -4), you can write it in point-slope form as y - (-4) = -3/2(x - -6). Distributing gives you y + 4 = (-3/2)x - 9, and subtracting 4 gives you y = (-3/2)x - 13. That calculation makes -13 the y-intercept, which is what the problem asks for.

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