AlgebraHardy-intercept of a perpendicular line through a point
Algebra practice question
In the xy-plane, line ℓ is perpendicular to the line y = 2x − 5 and passes through the point (4, 1). What is the y-coordinate of the point where line ℓ crosses the y-axis?
Answer: 3
A perpendicular to a line of slope 2 has slope −1/2. Through (4, 1): 1 = −(1/2)(4) + b, so b = 3.
Common wrong answers
- If you answered 1
- 1 is the y-coordinate of the given point, not of the intercept.
- If you answered -7
- −7 uses slope 2 (a parallel line): 1 = 2(4) + b.
- If you answered -1
- −1 uses slope 1/2, the wrong sign for a perpendicular.
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