Answer
$y-10=8(x-1)$
Work Step by Step
RECALL:
(1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$ is the slope and the line contains the point $(x_1, y_1)$.
(2) The slope of a line through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$$m=\dfrac{y_2-y_1}{x_2-x_1}$$
Solve for the slope of the line through the given points using the formula in (2) above to obtain:
\begin{align*}
m&=\dfrac{42-10}{5-1}\\\\
m&=\dfrac{32}{4}\\\\
m&=8
\end{align*}
Thus, using the point $(1, 10)$, the point-slope form of the line through the given two points is:
\begin{align*}
y-y_1&=m(x-x_1)\\
y-10&=8\left(x-1\right)
\end{align*}
