Question

Find the equation of the straight line which is parallel to $x-y=3$ and makes $x-$intercept $7$ units.

Answer 1

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

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

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

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

$x+k=0$

$\Rightarrow x=-k$

For the required member of the family which makes $x-$intercept $7$ units,

$-k=7\Rightarrow k=-7$

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

$x-y-7=0$