Answer
$4x+3y=2$
Work Step by Step
With the given points, $(-4,6)\text{ and } (2,-2),$ then
\begin{align*}\require{cancel}
y_1&=
6
,\\y_2&=
-2
,\\x_1&=
-4
,\text{ and }\\ x_2&=
2
.\end{align*}
Using $m=\dfrac{y_1-y_2}{x_1-x_2}$ or the Slope Formula, the slope, $m,$ of the line is
\begin{align*}
m&=\dfrac{6-(-2)}{-4-2}
\\\\&=
\dfrac{6+2}{-4-2}
\\\\&=
\dfrac{8}{-6}
\\\\&=
\dfrac{\cancel8^4}{-\cancel6^3}
\\\\&=
-\dfrac{4}{3}
.\end{align*}
Using $
y-y_1=m(x-x_1)
$ or the Point-Slope Form of linear equations, with the point $(-4,6)$ and $m=-\dfrac{4}{3},$ then
\begin{align*}
y-6&=-\dfrac{4}{3}(x-(-4))
\\\\
y-6&=-\dfrac{4}{3}(x+4)
.\end{align*}
Using the properties of equality, in the form $ax+by=c$ or the Standard Form of linear equations, the equation above is equivalent to
\begin{align*}
3(y-6)&=\left(-\dfrac{4}{3}(x+4)\right)3
\\\\
3(y-6)&=-4(x+4)
\\\\
3y-18&=-4x-16
\\\\
4x+3y-18&=-4x-16+4x
\\
4x+3y-18&=-16
\\
4x+3y-18+18&=-16+18
\\
4x+3y&=2
.\end{align*}
