Pencil line parallel to a given one

Text

In the pencil of lines through $P(-1,4)$, find the one parallel to $r:\;y=3x-2$.

Solution

Parallelism forces $m=3$. Impose that it passes through $P$: $y-4=3(x+1)\Rightarrow y=3x+7.$ $\boxed{\,y=3x+7\,}$