College Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 44

Find the equation of the line that has slope $\displaystyle -\frac{1}{2}$ and passes through the point $(6,-3)$ in...
a.) Slope intercept form.
b.) General form.

a.) Slope intercept form,

$
\begin{equation}
\begin{aligned}
y &= mx + b \\
\\
y &= -\frac{1}{2}x + b
\end{aligned}
\end{equation}
$

Solving for $b$ at point $(b,-3)$,

$
\begin{equation}
\begin{aligned}
-3 &= -\frac{1}{2} (6) + b\\
\\
-3 &= -3 + b\\
\\
b &= 0
\end{aligned}
\end{equation}
$

Thus the equation of the line is...
$\displaystyle y = -\frac{1}{2}x$

b.) General form,

$
\begin{equation}
\begin{aligned}
Ax + By + C &= 0 \\
\\
y &= - \frac{1}{2}x && \text{Multiply by } 2\\
\\
2y &= -x && \text{Add } x\\
\\
x + 2y &= 0
\end{aligned}
\end{equation}
$