1. **Problem:** Find the equation of the line passing through points (-3, -4) and (1, 4) in the form $y = mx + c$. 2. **Formula:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ The equation of the line is then: $$y = mx + c$$ where $c$ is the y-intercept. 3. **Calculate slope:** $$m = \frac{4 - (-4)}{1 - (-3)} = \frac{4 + 4}{1 + 3} = \frac{8}{4} = 2$$ 4. **Find $c$ using point (1,4):** $$4 = 2 \times 1 + c$$ $$4 = 2 + c$$ $$c = 4 - 2 = 2$$ 5. **Equation:** $$y = 2x + 2$$ --- 1. **Problem:** Find the equation of the line passing through points (0, -4) and (2, 4). 2. **Calculate slope:** $$m = \frac{4 - (-4)}{2 - 0} = \frac{8}{2} = 4$$ 3. **Find $c$ using point (0, -4):** $$-4 = 4 \times 0 + c$$ $$c = -4$$ 4. **Equation:** $$y = 4x - 4$$ --- 1. **Problem:** Find the equation of the line passing through points (-4, 4) and (2, -4). 2. **Calculate slope:** $$m = \frac{-4 - 4}{2 - (-4)} = \frac{-8}{6} = -\frac{4}{3}$$ 3. **Find $c$ using point (-4, 4):** $$4 = -\frac{4}{3} \times (-4) + c$$ $$4 = \frac{16}{3} + c$$ $$c = 4 - \frac{16}{3} = \frac{12}{3} - \frac{16}{3} = -\frac{4}{3}$$ 4. **Equation:** $$y = -\frac{4}{3}x - \frac{4}{3}$$ --- 1. **Problem:** Find the equation of the line passing through points (-4, -4) and (4, 4). 2. **Calculate slope:** $$m = \frac{4 - (-4)}{4 - (-4)} = \frac{8}{8} = 1$$ 3. **Find $c$ using point (-4, -4):** $$-4 = 1 \times (-4) + c$$ $$-4 = -4 + c$$ $$c = 0$$ 4. **Equation:** $$y = x$$