Answer
$y-10=-\frac{5}{2}(x+4)$
Work Step by Step
Recall:
(1) The slope $m$ of a line through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$$m=\dfrac{y_2-y_1}{x_2-x_1}$$
(2) The equation of a line whose slope is $m$ and passes through the point $(x_1, y_1)$ is:
$$y-y_1=m(x-x_1)$$
Solve for the slope using the formula in (1) above:
\begin{align*}
m&=\dfrac{15-10}{-6-(-4)}\\\\
&=\dfrac{5}{-6+4}\\\\
&=\dfrac{5}{-2}
\end{align*}
The line has $m=-\dfrac{5}{2}$ and passes through $(-4, 10)$.
Use the point-slope formula in (2) above to obtain the equation of the line:
\begin{align*}
y-10&=-\frac{5}{2}(x-(-4))\\\\
y-10&=-\frac{5}{2}(x+4)
\end{align*}
