How do you write an equation in point slope form that passes through (-2,-8) and parallel to line whose equation is y=-3x+2?

May 26, 2015

$y = - 3 x + 2$ is a linear equation in slope-intercept form with
slope $m = \left(- 3\right)$
(and y-intercept $= 2$)

We want the equation of a line with slope $m = \textcolor{red}{\left(- 3\right)}$ through the point $\left(\textcolor{b l u e}{- 2} , \textcolor{g r e e n}{- 8}\right)$

Using the point-slope linear equation form:
$\left(y - \textcolor{b l u e}{\left(- 8\right)}\right) = \textcolor{red}{\left(- 3\right)} \left(x - \textcolor{g r e e n}{\left(- 2\right)}\right)$

Simplifying
$y + 8 = - 3 x - 6$
or, in standard form
$3 x + y = - 14$