1. **State the problem:** Find the equation of the line passing through the points $(-4,40)$ and $(7,-20)$ in the form $y = mx + c$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** $$m = \frac{-20 - 40}{7 - (-4)} = \frac{-60}{7 + 4} = \frac{-60}{11}$$ 4. **Use point-slope form:** $$y - y_1 = m(x - x_1)$$ Using point $(-4,40)$: $$y - 40 = -\frac{60}{11}(x + 4)$$ 5. **Expand and simplify:** $$y - 40 = -\frac{60}{11}x - \frac{60}{11} \times 4$$ $$y - 40 = -\frac{60}{11}x - \frac{240}{11}$$ 6. **Add 40 to both sides:** $$y = -\frac{60}{11}x - \frac{240}{11} + 40$$ Convert 40 to fraction with denominator 11: $$40 = \frac{440}{11}$$ 7. **Combine constants:** $$y = -\frac{60}{11}x + \left(-\frac{240}{11} + \frac{440}{11}\right) = -\frac{60}{11}x + \frac{200}{11}$$ **Final answer:** $$y = -\frac{60}{11}x + \frac{200}{11}$$