College Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 50

Find the equation of the line that passes through the origin and is parallel to the line containing $(2,4)$ and $(4,-4)$ in
a.) Slope intercept form.
b.) General form.

a.) If the line is parallel to the line containing points $(2,4)$ and $(4,-4)$, then their slopes must be equal, so...
$\displaystyle m = \frac{y_2-y_1}{x_2-x_1} = \frac{-4-4}{4-2} = \frac{-8}{2} = - 4$

Then, if it passes through the origin, its $y$-intercept must be 0, so...
$y = mx + b$
$y = -4x + 0$

Thus, the equation of the line is...
$y = -4x$

b.) In general form,

$
\begin{equation}
\begin{aligned}
Ax + By + C &= 0 \\
\\
y &= -4x && \text{Add } 4x\\
\\
4x + y &= 0
\end{aligned}
\end{equation}
$