Answer
$a = \frac{3}{4}$
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:
$\frac{3}{4}a = \frac{9}{16}$
Let's solve for $a$ by dividing both sides by $\frac{3}{4}$. Dividing by a fraction means to multiply by its reciprocal; therefore, we multiply each side by the reciprocal of $\frac{3}{4}$ or $\frac{4}{3}$:
$a = (\frac{4}{3})(\frac{9}{16})$
Multiply to simplify:
$a = \frac{36}{48}$
Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is $12$:
$a = \frac{3}{4}$
