# Question #bce48

Feb 22, 2018

Parallel line, $y = - x - 1$ or $x + y = - 1$
Perpendicular line, $y = x + 5$

#### Explanation:

Let say ${m}_{1}$ is a gradient for line $x + y = 7$

$y = - x + 7$ $\to {m}_{1} = - 1$

since it is a parallel line, they have the same gradient value.
$\left(y - 2\right) = {m}_{1} \left(x - \left(- 3\right)\right)$
$y - 2 = - 1 \left(x + 3\right)$
$y = - x - 3 + 2$
$y = - x - 1$ or $x + y = - 1$

Assuming ${m}_{2}$ is a gradient for the perpendicular line thru point $\left(- 3 , 2\right)$, therefore

${m}_{1} \cdot {m}_{2} = - 1$
$- 1 \cdot {m}_{2} = - 1$ $\to {m}_{2} = 1$

for perpendicular line,
$\left(y - 2\right) = {m}_{2} \left(x - \left(- 3\right)\right)$
$y - 2 = 1 \left(x + 3\right)$
$y = x + 3 + 2$
$y = x + 5$