Question

Find the equation of the straight line which is parallel to $3x-5y=6$ and makes $x-$intercept $\frac{-3}{2}$ units.

Answer 1

The given line is $3x-5y=6$ .......$\left(1\right)$

The equation of the family of lines parallel to $\left(1\right)$ is

$3x-5y+k=0$ .....$\left(2\right)$ where $k$ is a parameter.

To find $x-$intercept,put $y=0$ in $\left(2\right)$ we get

$3x+k=0$

$\Rightarrow x=\frac{-k}{3}$

For the required member of the family which makes $x-$intercept $\frac{-3}{2}$ units,

$\frac{-k}{3}=\frac{-3}{2}\Rightarrow k=\frac{9}{2}$

Substituting this value of $k$ in $\left(2\right)$, the equation of the required line is

$3x-5y+\frac{9}{2}=0$ or $6x-10y+9=0$