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


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