Oct 10, 2016

$y = - 7 x - 22$

#### Explanation:

The point-slope form of the equation of a line with slope $m$ which passes through the point $\left({x}_{1} , {y}_{1}\right)$ is

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

In the above exercise, we have $m = - 7$ and $\left({x}_{1} , {y}_{1}\right) = \left(- 2 , - 8\right)$. Plugging those into our formula, we get

$y - \left(- 8\right) = - 7 \left(x - \left(- 2\right)\right)$

$\implies y + 8 = - 7 \left(x + 2\right)$

$\implies y + 8 = - 7 x - 14$

$\therefore y = - 7 x - 22$