AlgebraVery hardIntercept of a perpendicular partner line
Algebra practice question
In the xy-plane, the lines y = ax + 2 and y = 3x + b, where a and b are constants, are perpendicular and intersect at a point with x-coordinate 3. What is the value of b?
Answer: -8
Perpendicular to slope 3 means a = −1/3, so at x = 3 the first line gives y = 1. Then 1 = 9 + b, so b = −8.
Common wrong answers
- If you answered 2
- 2 copies the other line's intercept.
- If you answered 8
- 8 has the sign wrong.
- If you answered -7
- −7 uses y = 2 at x = 3.
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