Line Slope Intercept 9F33D4

1. **State the problem:** We need to find the equation of a line in slope-intercept form, which is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 2. **Given:** Slope $m = -\frac{4}{5}$ and point $(-5, -4)$ lies on the line. 3. **Use the point-slope form:** $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is the given point. 4. Substitute the values: $$y - (-4) = -\frac{4}{5}(x - (-5))$$ which simplifies to $$y + 4 = -\frac{4}{5}(x + 5)$$. 5. Distribute the slope: $$y + 4 = -\frac{4}{5}x - \frac{4}{5} \times 5$$. 6. Simplify the multiplication: $$y + 4 = -\frac{4}{5}x - 4$$. 7. Subtract 4 from both sides to isolate $y$: $$y + 4 - 4 = -\frac{4}{5}x - 4 - 4$$. 8. Use cancellation notation: $$y + \cancel{4} - \cancel{4} = -\frac{4}{5}x - 8$$. 9. Final slope-intercept form: $$y = -\frac{4}{5}x - 8$$. **Answer:** The equation of the line is $$y = -\frac{4}{5}x - 8$$.