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}$