Question

The equation of the line passing through the point $(2,-3)$ and parallel to the line joining the points $(1,2)$ and $(-1,5)$ is

• A. $3x+2y=0$
• B. $2x+3y-1=0$
• C. $x-3y+6=0$
• D. $x+3y+12=0$

Answer 1

The correct option is A $3x+2y=0$

Equation of the line joining points: $(1,2)$ and $(-1,5):$

$y-5=\left(\frac{-3}{2}\right)(x+1)$

$y-5=\frac{-3x}{2}-\frac{3}{2}$

$\Rightarrow y=\frac{-3x}{2}-\frac{3}{2}+5$

$\Rightarrow y=\frac{-3x}{2}+\frac{7}{2}$

Equation of the line passing through the point $(2,-3)$ and parallel to the line joining points: $(1,2)$ and $(-1,5)$:

$y+3=\frac{-3}{2}(x-2)$

$\Rightarrow y+3=\frac{-3x}{2}+3$

$\Rightarrow y=\frac{-3x}{2}$

$\therefore 2y+3x=0$ is the required equaiton of the line.