AlgebraHardIntercept of a perpendicular line
Algebra practice question
In the xy-plane, line n is perpendicular to the line y = 4x and passes through the point (8, 1). What is the y-intercept of line n?
Answer: 3
A line perpendicular to slope 4 has slope −1/4. So y = −(1/4)x + b, and 1 = −2 + b gives b = 3.
Common wrong answers
- If you answered 1
- 1 is the y-coordinate of the given point, not the intercept.
- If you answered -1
- −1 comes from 1 = 2 + b, using slope +1/4; the perpendicular slope is −1/4.
- If you answered -31
- −31 comes from using slope 4 (parallel, not perpendicular): 1 = 32 + b.
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