Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 12

Using the slope intercept form, determine the equation of the line that contains the point whose coordinates are $(5,-1)$ and has slope of $\displaystyle \frac{1}{5}$.


$\begin{equation} \begin{aligned} y =& mx+b && \\ y =& \frac{1}{5}x + b && \text{Replace $m$ with } \frac{1}{2} \\ -1 =& \frac{1}{5} (5) + b && \text{Substitute $x = 5$ and $y = -1$} \\ -1 =& 1 + b && \text{Solve for } b \\ \\ -2 =& b && \text{Add } -1 \\ \\ y =& \frac{1}{5} x - 2 && \text{Write the equation of the line by replacing $m$ and $b$ in $y = mx+ b$ by their values} \end{aligned} \end{equation}$