Answer
$$
m=\frac{5}{9}
.$$
Work Step by Step
Rewrite the equation in the slope-intercept form $y=mx+c$ as follows:
$$
-9y=-5x-2\Longrightarrow y=\frac{5}{9}x+\frac{2}{9}
.$$
Now, by comparing the given equation with the standard slope-intercept form $y=mx+c$, we find that the slope is
$$
m=\frac{5}{9}
.$$
