Answer
$y+3=\dfrac{5}{3}(x+4)$
Work Step by Step
With the given points, $(-4,-3)\text{ and } (2,7),$ then
\begin{align*}
y_1&=
-3
,\\y_2&=
7
,\\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*}\require{cancel}
m&=\dfrac{-3-7}{-4-2}
\\\\&=
\dfrac{-10}{-6}
\\\\&=
\dfrac{\cancel{-10}^5}{\cancel{-6}^3}
\\\\&=
\dfrac{5}{3}
.\end{align*}
Using $
y-y_1=m(x-x_1)
$ or the Point-Slope Form of linear equations, with the point $(-4,-3)$ and $m=\dfrac{5}{3},$ then
\begin{align*}
y-(-3)&=\dfrac{5}{3}(x-(-4))
\\\\
y+3&=\dfrac{5}{3}(x+4)
.\end{align*}
Hence, an equation of the line in Point-Slope Form is $
y+3=\dfrac{5}{3}(x+4)
.$
