Question

Find the equation of the line parallel to the line $3x+2y=8$ and passing through the point $(0,1)$.

• A. 2x+3y-2=0
• B. 3x+2y-2=0
• C. 3x+2y-3=0
• D. 3x+2y+3=0

Answer 1

The correct option is B

3x+2y-2=0

We have, $3x+2y=8$
$\Rightarrow 2y=8-3x\Rightarrow y=\frac{-3}{2}x+4$
$\therefore$ Slope of the line, $m=-\frac{3}{2}$
Since the required line is parallel to the given line
$\therefore$ Slope of the required line $=-\frac{3}{2}$
$\therefore$ Equation of the line passing through (0,1) and having slope $-\frac{3}{2}$ is given by,
$y-y_1=m(x-x_1)$
$\Rightarrow y-1=-\frac{3}{2}(x-0)$
$\Rightarrow 2y-2+3x=0$
$\Rightarrow 3x+2y-2=0$, which is the required line.