1. **State the problem:** Write an equation in slope-intercept and standard form that passes through the point $(5, -5)$ and is parallel to $y = -\frac{7}{5}x - 5$. 2. **Identify the slope:** Since the line must be parallel to $y = -\frac{7}{5}x - 5$, it has the same slope $m = -\frac{7}{5}$. 3. **Use the point-slope form:** The formula is $y - y_1 = m(x - x_1)$ where $(x_1, y_1) = (5, -5)$. 4. **Substitute values:** $$y - (-5) = -\frac{7}{5}(x - 5)$$ which simplifies to $$y + 5 = -\frac{7}{5}x + 7$$ 5. **Solve for $y$ to get slope-intercept form:** $$y = -\frac{7}{5}x + 7 - 5$$ $$y = -\frac{7}{5}x + 2$$ 6. **Convert to standard form:** Multiply both sides by 5 to clear the fraction: $$5y = -7x + 10$$ Rearranged: $$7x + 5y = 10$$ 7. **Check for simplification:** No common factors to cancel. **Final answers:** - Slope-intercept form: $y = -\frac{7}{5}x + 2$ - Standard form: $7x + 5y = 10$