1. **State the problem:** Find the equation of the line passing through the points $(1,-5)$ and $(9,11)$. 2. **Formula used:** The equation of a line in slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1) = (1,-5)$ and $(x_2,y_2) = (9,11)$. $$m = \frac{11 - (-5)}{9 - 1} = \frac{11 + 5}{8} = \frac{16}{8} = 2$$ 4. **Find the y-intercept $b$:** Substitute one point and the slope into $y = mx + b$. Using $(1,-5)$: $$-5 = 2(1) + b \implies -5 = 2 + b \implies b = -5 - 2 = -7$$ 5. **Write the equation:** Substitute $m=2$ and $b=-7$ into $y = mx + b$: $$y = 2x - 7$$ **Final answer:** The equation of the line is $y = 2x - 7$.