Find the equation of the line that is perpendicular to $3 x + 4 y = 12$ and passes through the point $(2, - 1)$ .

medium 3 marks Class 9 · Mathematics · Coordinate Geometry

Answer

4 x - 3 y = 11

The correct answer is $4 x - 3 y = 11$ — Thus the required line is $4 x - 3 y = 11$ .

Step-by-step solution

Rewrite $3 x + 4 y = 12$ in slope‑intercept form: $y = - \frac{3}{4} x + 3$ to read slope $m_{1} = - \frac{3}{4}$ .
The perpendicular slope is $m_{2} = - 1/ m_{1} = \frac{4}{3}$ .
Apply point‑slope form with $(2, - 1)$ : $y - (- 1) = \frac{4}{3} (x - 2)$ .
Simplify: $y + 1 = \frac{4}{3} x - \frac{8}{3}$ .
Subtract 1: $y = \frac{4}{3} x - \frac{11}{3}$ .
Convert to standard form: multiply by 3 → $3 y = 4 x - 11$ so $4 x - 3 y = 11$ .
Thus the required line is $4 x - 3 y = 11$ .

Common mistake: taking incorrect negative reciprocal or missing sign in the equation

Concept tested: perpendicular line equation