Question

The equation of a line which is parallel to the line $3x-5y+8=0$ and making an intercept $-3$ on $x-$ axis is

• A. $5y-3x=9$
• B. $5y+3x=9$
• C. $3x+5y=9$
• D. $3x-5y=9$
• E. $noneofthese$

Answer 1

The correct option is D $3x-5y=9$

Let $3x-5y+8=0$ be the line

Slope of $5y=3x+8$ or $y=\frac{3}{5}x+\frac{8}{5}$ is $\frac{3}{5}$

We know that parallel lines have equal slopes,

$\therefore$ the slope of the other line which is parallel to the given line is $\frac{3}{5}$

The point is $(-3,0)$

Equation of the line is $y=mx+c$

$\Rightarrow 0=\frac{3}{5}\times -3-c$

$\Rightarrow c=\frac{-9}{5}$

$\therefore$ equation of the line is $y=\frac{3}{5}x+\left(\frac{-9}{5}\right)$

or $5y=3x-9$

or $5y-3x=-9$

or $3x-5y=9$