Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 28

Using the point slope formula, find the equation of the line that passes through the point whose coordinates are $(-5,0)$ and has slope of $\displaystyle \frac{-1}{5}$


$\begin{equation} \begin{aligned} (x_1, y_1) =& (-5,0) && \text{Let $(x_1, y_1)$ be the given point} \\ m =& \frac{-1}{5} && \text{$m$ is the given slope} \\ y - y_1 =& m(x- x_1) && \text{Point slope formula} \\ y -0 =& \frac{-1}{5} [x-(-5)] && \text{Substitute $-5$ for $x$, $$ for $y$ and } \frac{-1}{5} \text{ for $m$} \\ y =& \frac{-1}{5} ( x + 5) && \text{Rewrite the equation in the form } y = mx+b \\ y =& \frac{-1}{5} x - 1 && \end{aligned} \end{equation}$