Answer
$a = -\frac{1}{6}$
Work Step by Step
This equation is in slope-intercept form, which is given by the formula:
$y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept of the line.
If we look at the equation we are given, $y = -3ax - 4$, then $-3a$ would be $m$, our slope.
We know that the actual value for our slope is $m = \frac{1}{2}$, so we set $-3a$ equal to $\frac{1}{2}$, and then solve for $a$:
$-3a = \frac{1}{2}$
To solve for $a$, we divide both sides of the equation by $-3$, which means that we multiply by the reciprocal, which is $-\frac{1}{3}$:
$(-\frac{1}{3})(-3)a = (-\frac{1}{3})(\frac{1}{2})$
Multiply to simplify:
$a = -\frac{1}{6}$
