Prow that the line through the point `(x_1> y_1)` and parallel to the line `A x+B y+C=0` is `A(x-x_1)+B(y-y_1)=0` .

Explanation

Let equation of a line parallel to line `Ax+By+C=0` is ,
`Ax+By=lambda` ………`(1)`
This line passes through the point `(x_(1),y_(1))`,
`:. Ax_(1)+By_(1)=lambda`
Put this value of `lambda` in equation `(1)`,
`Ax+By=Ax_(1)+By_(1)`
`impliesA(x-x_(1))+B(y-y_(1))=0`