Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 14

Using the slope intercept form, determine the equation of the line that contains the point whose coordinates are $(-1,2)$ 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} \\ 2 =& \frac{-1}{2} (-1) + b && \text{Substitute $x = -1$ and $y = 2$} \\ 2 =& \frac{1}{2} + b && \text{Solve for } b \\ \\ \frac{3}{2} =& b && \text{Add } \frac{-1}{2} \\ \\ y =& \frac{-1}{2} x + \frac{3}{2} && \text{Write the equation of the line by replacing $m$ and $b$ in $y = mx+ b$ by their values} \end{aligned} \end{equation}$