NumericalModerate3 marks
If the straight lines 3x - 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another, find the value of a.
Topic: Slope and equation of a line
Previous-year question practice database
Answer
Solution diagram
Exam answer
3x − 5y = 7 ⇒ y = (3/5)x − 7/5 so m₁ = 3/5.
4x + ay + 9 = 0 ⇒ y = (−4/a)x − 9/a so m₂ = −4/a.
Perpendicular lines satisfy: m₁m₂ = −1.
(3/5)(−4/a) = −1 a = 12/5 = 2.4.
Answer: a = 12/5.
Explanation
Convert both lines to slope-intercept form. Perpendicular slopes multiply to −1.
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