Answer
$a = 9$
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, $y = \frac{2}{9}ax + 6$, then $\frac{2}{9}a$ would be $m$, our slope. We know that the actual value for our slope is $m = 2$, so we set $\frac{2}{9}a$ equal to $2$, and then solve for $a$:
$\frac{2}{9}a = 2$
To solve for $a$, we divide both sides of the equation by $\frac{2}{9}$, which means that we multiply by the reciprocal, which is $\frac{9}{2}$:
$(\frac{9}{2})(\frac{2}{9})a = 2(\frac{9}{2})$
Multiply to simplify:
$a = \frac{18}{2}$
Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is $2$:
$a = 9$
