Question

Find the equation of the straight line which is parallel to $2x-3y=5$ and makes $x-$intercept $\frac{1}{2}$ units.

Answer 1

The given line is $2x-3y=5$ .......$\left(1\right)$

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

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

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

$2x+k=0$

$\Rightarrow x=\frac{-k}{2}$

For the required member of the family which makes $x-$intercept $\frac{1}{2}$ units,

$\frac{-k}{2}=\frac{1}{2}\Rightarrow k=-1$

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

$2x-3y-1=0$