AlgebraHardPerpendicular line's equation
Algebra practice question
Line k in the xy-plane has equation y = −(1/4)x + 2. Which of the following is an equation of a line perpendicular to line k?
- A. y = 4x − 1Correct
- B. y = −4x + 2
- C. y = (1/4)x + 5
- D. y = −(1/4)x − 3
Answer: A. y = 4x − 1
Perpendicular slopes are negative reciprocals: the negative reciprocal of −1/4 is 4. Only y = 4x − 1 has slope 4.
Why the other answers are wrong
- B. y = −4x + 2
- −4 is the reciprocal with the wrong sign; −1/4 × −4 = 1, not −1.
- C. y = (1/4)x + 5
- 1/4 is the opposite sign but not the reciprocal.
- D. y = −(1/4)x − 3
- −1/4 is the same slope, which makes the line PARALLEL to k.
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