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}
$