Find the equation of the line that passes through the point $(6, - 2)$ and is parallel to the line joining the points $(1, 1)$ and $(4, 7)$ . Write the final equation in the form ax+by+c=0.

medium 3 marks Class 10 · Mathematics · Coordinate Geometry

Answer

2 x - y - 14 = 0

The correct answer is $2 x - y - 14 = 0$ — Thus the equation of the required line is $2 x - y - 14 = 0$ .

Step-by-step solution

First find the slope of the line through $(1, 1)$ and $(4, 7)$ using $m = \frac{7 - 1}{4 - 1} = \frac{6}{3} = 2$ .
Since parallel lines have equal slopes, the required line also has slope $m = 2$ .
Use point‑slope form with point $(6, - 2)$ : $y - (- 2) = 2 (x - 6)$ .
Simplify: $y + 2 = 2 x - 12$ .
Bring all terms to one side: $2 x - y - 14 = 0$ .
Thus the equation of the required line is $2 x - y - 14 = 0$ .

Common mistake: Using the slope of a different line or mixing up the given point while applying point‑slope form.

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