Which of the following is the correct equation of the line that passes through the point $(3, - 1)$ and is parallel to the line $2 x - y + 5 = 0$ ? Write the equation in the form $a x + b y + c = 0$ .

medium MCQ 2 marks Class 10 · Mathematics · Coordinate Geometry

$2 x - y - 7 = 0$
$2 x + y - 7 = 0$
$- 2 x + y + 7 = 0$
$2 x - y + 7 = 0$

Answer

2 x - y - 7 = 0

The correct answer is $2 x - y - 7 = 0$ — Bring all terms to the left to obtain $2 x - y - 7 = 0$ , which matches the required $a x + b y + c = 0$ format.

Step-by-step solution

Rewrite the given line $2 x - y + 5 = 0$ in slope‑intercept form: $y = 2 x + 5$ , so its slope $m = 2$ .
Parallel lines have the same slope; therefore the required line also has slope $m = 2$ .
Use the point‑slope form with point $(3, - 1)$ : $y - (- 1) = 2 (x - 3)$ , i.e., $y + 1 = 2 x - 6$ .
Bring all terms to the left to obtain $2 x - y - 7 = 0$ , which matches the required $a x + b y + c = 0$ format.

Common mistake: Using the wrong sign for the constant term after rearranging the equation.

Concept tested: Equation of a line parallel to a given line

Published 23 August 2026 · Last updated 24 August 2026 · How this solution was prepared and checked

Which of the following is the correct equation of the line that passes through the point (3,−1) and is parallel to the line 2x−y+5=0? Write the equation in the form ax+by+c=0.

Step-by-step solution

Related questions

Which of the following is the correct equation of the line that passes through the point $(3, - 1)$ and is parallel to the line $2 x - y + 5 = 0$ ? Write the equation in the form $a x + b y + c = 0$ .