1. **State the problem:** Put the equation $12y - 9x = -36$ into slope-intercept form $y = mx + b$. 2. **Recall the slope-intercept form:** The slope-intercept form of a line is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Isolate $y$ on one side:** Starting with $$12y - 9x = -36$$ add $9x$ to both sides: $$12y = 9x - 36$$ 4. **Divide both sides by 12 to solve for $y$:** $$y = \frac{9x - 36}{12}$$ 5. **Simplify the fraction by dividing numerator and denominator by 3:** $$y = \frac{\cancel{3} \times 3x - \cancel{3} \times 12}{\cancel{3} \times 4} = \frac{3x - 12}{4}$$ 6. **Split the fraction:** $$y = \frac{3x}{4} - \frac{12}{4}$$ 7. **Simplify the constants:** $$y = \frac{3}{4}x - 3$$ **Final answer:** $$y = \frac{3}{4}x - 3$$