Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 10

Using the slope intercept form, determine the equation of the line that contains the point whose coordinates are $(2,3)$ and has slope of $\displaystyle \frac{-1}{2}$.


$\begin{equation} \begin{aligned} y =& mx+b && \\ y =& \frac{-1}{2}x + b && \text{Replace $m$ with } \frac{1}{2} \\ 3 =& \frac{-1}{2} (2) + b && \text{Substitute $x = 2$ and $y = 3$} \\ 3 =& -1 + b && \text{Solve for } b \\ \\ 4 =& b && \text{Add } 1 \\ \\ y =& \frac{-1}{2}x + 4 && \text{Write the equation of the line by replacing $m$ and $b$ in $y = mx+ b$ by their values} \end{aligned} \end{equation}$