Answer
$y=-\frac{4}{3}x-4$
Work Step by Step
RECALL:
(i)
The y-intercept is the y-coordinate of the point where a line passes through the y-axis.
(ii)
The slope-intercept form of the equation of a line is:
$y=mx+b$
where
m=slope
b=y-intercept
The given line passes through the y-axis at $(0, -4)$ therefore its y-intercept is $-4$.
This means that the tentative equation of the given line is
$y=mx - 4$
The line contains the point $(-3, 0)$, to the coordinates of this point satisfy the equation of the line.
Substitute the x and y coordinates of this point into the tentative equation of the line to have:
$y=mx-4
\\0=m(-3)-4
\\0=-3m-4
\\3m=-4
\\m=-\frac{4}{3}$
Therefore, the equation of the line is $y=-\frac{4}{3}x-4$.
