1. **State the problem:** Find the slope $m$ of the line given by the equation $$9x - 6y = -9.$$\n\n2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b,$$ where $m$ is the slope and $b$ is the y-intercept.\n\n3. **Isolate $y$ in the equation:**\n$$9x - 6y = -9$$\nSubtract $9x$ from both sides:\n$$-6y = -9 - 9x$$\nRewrite as:\n$$-6y = -9x - 9$$\n\n4. **Divide both sides by $-6$ to solve for $y$:**\n$$y = \frac{-9x - 9}{-6}$$\nShow cancellation of common factors:\n$$y = \frac{\cancel{-9}x + \cancel{-9}}{\cancel{-6}}$$\nSince $-9/-6 = 3/2$, rewrite as:\n$$y = \frac{3}{2}x + \frac{3}{2}$$\n\n5. **Identify the slope:** The coefficient of $x$ is the slope $m$, so\n$$m = \frac{3}{2}.$$\n\n**Final answer:** The slope of the line is $m = \frac{3}{2}$.