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