1. **Problem statement:** Write the equation of a line in slope-intercept form that passes through the points $(-1, 3)$ and $(4, 13)$. 2. **Formula used:** The slope $m$ of a line passing 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 a line in point-slope form is: $$y - y_1 = m(x - x_1)$$ which can be rearranged to slope-intercept form: $$y = mx + b$$ where $b$ is the y-intercept. 3. **Calculate the slope:** $$m = \frac{13 - 3}{4 - (-1)} = \frac{10}{5} = 2$$ 4. **Use point-slope form with point $(-1, 3)$:** $$y - 3 = 2(x - (-1))$$ 5. **Simplify the expression:** $$y - 3 = 2(x + 1)$$ $$y - 3 = 2x + 2$$ 6. **Isolate $y$ to get slope-intercept form:** $$y = 2x + 2 + 3$$ $$y = 2x + 5$$ **Final answer:** $$y = 2x + 5$$ This means the line has slope 2 and crosses the y-axis at 5.