Question

When given line `y=2x + 3` and point (4,2), how would you find a parallel and a perpendicular line?

Answer 1

Let say that `y=mx+b` is the parallel to `y=2x+3` from point `(4,2)`

Hence `2=4m+b` where `m=2` hence `b=-6` so the line is

`y=2x-6`.

The perpendicular line is `y=kx+c` where `k*2=-1=>k=-1/2` hence

`y=-1/2x+c`.Because point `(4,2)` statisfies the equation we have that

`2=-1/2*4+c=>c=4`

Hence the perpendicular is `y=-1/2x+4`