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

Let say that $y = m x + b$ is the parallel to $y = 2 x + 3$ from point $\left(4 , 2\right)$

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

$y = 2 x - 6$.

The perpendicular line is $y = k x + c$ where $k \cdot 2 = - 1 \implies k = - \frac{1}{2}$ hence

$y = - \frac{1}{2} x + c$.Because point $\left(4 , 2\right)$ statisfies the equation we have that

$2 = - \frac{1}{2} \cdot 4 + c \implies c = 4$

Hence the perpendicular is $y = - \frac{1}{2} x + 4$