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}
$