Precalculus, Chapter 1, 1.3, Section 1.3, Problem 60

Determine the equation of the line that is parallel to the line $y = -3x$ containing the point $(-1,2)$. Express your answer using the general form or the slope intercept form of the equation of a line, which ever you prefer.

Since the two lines are parallel, the slope of the line that we
need, equals the slope of the line $y = -3x$. The equation is in
slope intercept form where in the slope is $-3$. So the other also
has slope $-3$ and contains the point $(-1,2)$. By using Point
Slope Form to find the equation



$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x- x_1)
&& \text{Point Slope Form}
\\
y - 2 =& -3 [x - (-1)]
&& \text{Substitute $m = -3, x = -1$ and $y = 2$}
\\
y =& -3x-3+2
&& \text{Simplify}
\\
y =& -3x-1
&& \text{Slope Intercept Form}
\\
\text{or} &
&&
\\
3x + y =& -1
&& \text{General Form}


\end{aligned}
\end{equation}
$