Find the equation of the line that passes through the point $(4, - 3)$ and is parallel to the line $2 x - 5 y + 7 = 0$ .

medium 3 marks Class 10 · Mathematics · Coordinate Geometry

Answer

2 x - 5 y - 23 = 0

The correct answer is $2 x - 5 y - 23 = 0$ — Bring all terms to one side: $2 x - 5 y - 23 = 0$ .

Step-by-step solution

Rewrite the given line in slope‑intercept form: $2 x - 5 y + 7 = 0 \Rightarrow - 5 y = - 2 x - 7 \Rightarrow y = \frac{2}{5} x + \frac{7}{5}$ .
Hence the slope of any line parallel to it is $m = \frac{2}{5}$ .
Use the point‑slope form with point $(4, - 3)$ : $y - (- 3) = \frac{2}{5} (x - 4)$ .
Simplify: $y + 3 = \frac{2}{5} x - \frac{8}{5}$ .
Multiply by 5: $5 y + 15 = 2 x - 8$ .
Bring all terms to one side: $2 x - 5 y - 23 = 0$ .

Common mistake: Using the wrong sign for the slope or not simplifying the constant term correctly.

Concept tested: Equation of a line – parallelism