1. **State the problem:** Find the equation of the line in point-slope and slope-intercept form given points (-2, -5) and (5, 0). 2. **Find the slope $m$ using the formula:** $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (-2, -5)$ and $(x_2, y_2) = (5, 0)$. 3. **Calculate the slope:** $$m = \frac{0 - (-5)}{5 - (-2)} = \frac{0 + 5}{5 + 2} = \frac{5}{7}$$ 4. **Write the point-slope form:** $$y - y_1 = m(x - x_1)$$ Substitute $m = \frac{5}{7}$ and point $(-2, -5)$: $$y - (-5) = \frac{5}{7}(x - (-2))$$ which simplifies to $$y + 5 = \frac{5}{7}(x + 2)$$ 5. **Convert to slope-intercept form $y = mx + b$:** Distribute the slope: $$y + 5 = \frac{5}{7}x + \frac{5}{7} \times 2 = \frac{5}{7}x + \frac{10}{7}$$ Subtract 5 from both sides: $$y = \frac{5}{7}x + \frac{10}{7} - 5$$ Rewrite 5 as $\frac{35}{7}$: $$y = \frac{5}{7}x + \frac{10}{7} - \frac{35}{7} = \frac{5}{7}x - \frac{25}{7}$$ **Final answers:** - Point-slope form: $$y + 5 = \frac{5}{7}(x + 2)$$ - Slope-intercept form: $$y = \frac{5}{7}x - \frac{25}{7}$$