1. **State the problem:** Put the equation $3x - 6y = -30$ into slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Isolate $y$:** Start by moving the $3x$ term to the right side by subtracting $3x$ from both sides: $$3x - 6y - 3x = -30 - 3x$$ which simplifies to $$-6y = -30 - 3x$$ 3. **Divide both sides by $-6$ to solve for $y$:** $$\cancel{-6}y = \frac{-30 - 3x}{\cancel{-6}}$$ This becomes $$y = \frac{-30}{-6} + \frac{-3x}{-6}$$ 4. **Simplify the fractions:** $$y = 5 + \frac{1}{2}x$$ 5. **Rewrite in slope-intercept form:** $$y = \frac{1}{2}x + 5$$ **Final answer:** The slope-intercept form is $y = \frac{1}{2}x + 5$.