Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 36

Determine the equation of the line through the points whose coordinates are $(1,5)$ and $(3,9)$.

Using the Slope Formula with $(x_1, y_1) = (1,5)$ and $(x_2, y_2) = (3,9)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9-5}{3-1} = \frac{4}{2} = 2$

The slope of the line is $2$.

Using the point slope formula with $m = 2$ and $(x_1, y_1) = (1,5)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
y - 5 =& 2(x-1)
&& \text{Substitute } m = 2, (x_1, y_1) = (1,5)
\\
y-5 =& 2x-2
&& \text{Apply Distributive Property}
\\
y =& 2x+3
&& \text{Write the slope-intercept form}

\end{aligned}
\end{equation}
$