1. **Problem:** Find the rate of change (slope) and y-intercept of the line given by the equation $5x - 15y = -10$. 2. **Rewrite the equation in slope-intercept form $y = mx + b$:** $$5x - 15y = -10$$ Subtract $5x$ from both sides: $$-15y = -5x - 10$$ Divide both sides by $-15$: $$y = \frac{-5x - 10}{-15}$$ Show cancellation: $$y = \frac{\cancel{-5}x + \cancel{10}}{\cancel{-15}} = \frac{5}{15}x + \frac{10}{15}$$ Simplify fractions: $$y = \frac{1}{3}x + \frac{2}{3}$$ 3. **Interpretation:** - Rate of change (slope) $m = \frac{1}{3}$ - Y-intercept $b = \frac{2}{3}$ **Final answer:** The rate of change is $\frac{1}{3}$ and the y-intercept is $\frac{2}{3}$.