Precalculus, Chapter 1, 1.3, Section 1.3, Problem 50

Determine an equation for the line containing the points $(-3,4)$ and $(2,5)$. Express your answer using the general form or the slope intercept form of the equation of a line, which ever you prefer.

Using the Formula for Slope $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1) = (-3,4)$ and $(x_2, y_2) = (2,5)$. We have

$\displaystyle m = \frac{5-4}{2-(-3)} = \frac{1}{5}$

The slope is $\displaystyle \frac{1}{5}$

Using the Point Slope Form to find the equation


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x- x_1)
&& \text{Point Slope Form}
\\
\\
y - 4 =& \frac{1}{5} [x - (-3)]
&& \text{Substitute } m = \frac{1}{5}, x = -3 \text{ and } y = 4
\\
\\
y =& \frac{1}{5}x + \frac{3}{5} + 4
&& \text{Simplify}
\\
y =& \frac{1}{5}x + \frac{23}{5}
&& \text{Slope Intercept Form}


\end{aligned}
\end{equation}
$