1. **State the problem:** Solve the equation $2x - 5y = -7$ for $y$ in 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 $2x$ to the right side: $$-5y = -2x - 7$$ 3. **Divide both sides by $-5$ to solve for $y$:** $$y = \frac{-2x - 7}{-5}$$ 4. **Simplify the fraction:** $$y = \frac{\cancel{-2}x + \cancel{-7}}{\cancel{-5}} = \frac{2}{5}x + \frac{7}{5}$$ 5. **Final slope-intercept form:** $$y = \frac{2}{5}x + \frac{7}{5}$$ This means the slope $m$ is $\frac{2}{5}$ and the y-intercept $b$ is $\frac{7}{5}$.