1. **State the problem:** Find the equation of the line passing through the points $(-1, -3)$ and $(1, 11)$. 2. **Formula used:** The slope $m$ of a line through two 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 in slope-intercept form is: $$y = mx + b$$ where $b$ is the y-intercept. 3. **Calculate the slope:** $$m = \frac{11 - (-3)}{1 - (-1)} = \frac{11 + 3}{1 + 1} = \frac{14}{2} = 7$$ 4. **Find the y-intercept $b$:** Use one of the points, for example $(1, 11)$, and plug into $y = mx + b$: $$11 = 7 \times 1 + b$$ $$11 = 7 + b$$ $$b = 11 - 7 = 4$$ 5. **Write the equation of the line:** $$y = 7x + 4$$ **Final answer:** The equation of the line passing through $(-1, -3)$ and $(1, 11)$ is: $$y = 7x + 4$$