maths

The given line is $x−y=3$ .......$(1)$

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

$x−y+k=0$ .....$(2)$ where $k$ is a parameter.

To find $x−$intercept,put $y=0$ in $(2)$ we get

$x+k=0$

$⇒x=−k$

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

$−k=7⇒k=−7$

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

$x−y−7=0$

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