Answer
$a = -5$
Work Step by Step
The equation is already in slope intercept form, which is given by the formula:
$y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
We can see that the coefficient of the variable $x$ would be the slope. We set this coefficient equal to the slope $m$ that we are given:
$-\frac{1}{2}a = \frac{5}{2}$
Let's solve for $a$ by dividing both sides by $-\frac{1}{2}$. Dividing by a fraction means multiplying by its reciprocal; therefore, we multiply each side by the reciprocal of $-\frac{1}{2}$ or $-2$:
$a = -2(\frac{5}{2})$
Multiply to simplify:
$a = -\frac{10}{2}$
Simplify the fraction:
$a = -5$