AlgebraHardy-intercept of a perpendicular through the second of two points
Algebra practice question
In the xy-plane, line ℓ passes through the points (2, 3) and (6, 11). Line m is perpendicular to ℓ and passes through (6, 11). What is the y-intercept of line m?
Answer: 14
Slope of ℓ = (11 − 3)/(6 − 2) = 2, so line m has slope −1/2. Through (6, 11): 11 = −(1/2)(6) + b → b = 14.
Common wrong answers
- If you answered 8
- 8 uses slope +1/2.
- If you answered 23
- 23 uses slope 2 with a sign slip: 11 + 12.
- If you answered -1
- −1 is the y-intercept of line ℓ.
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