Answer
$y=-\dfrac{4}{3}x-4$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ = slope and $b$ = y-intercept.
(2) The slope of a line is equal to $\dfrac{rise}{run}$.
Given two points on the line, rise is the increase (or decrease) in the y-value while run is the increase (or decrease) in the x-value.
The line passes through the point $(0, -4)$ therefore the y-intercept is $-4$.
The line also passes through the point $(-3, 0)$.
Note that from $(-3, 0)$ to $(0, -4)$, there is a:
decrease in y-value of 4 units $\longrightarrow \text{rise} = -4$
increase in x-value of 3 units $\longrightarrow \text{run} = 3$
Thus, the slope is:
$=\dfrac{rise}{run} = \dfrac{-4}{3}=-\dfrac{4}{3}$
With $b=-4$ and $m=-\dfrac{4}{3}$, the equation of the line is:
$y=mx + b
\\y = -\dfrac{4}{3}x + (-4)
\\y=-\dfrac{4}{3}x-4$
