1. **State the problem:** Find the equation of the line passing through points $(-7, -3)$ and $(-2, 4)$. 2. **Formula used:** 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 line equation in slope-intercept form is $$y = mx + b$$ where $b$ is the y-intercept. 3. **Calculate the slope:** $$m = \frac{4 - (-3)}{-2 - (-7)} = \frac{4 + 3}{-2 + 7} = \frac{7}{5}$$ 4. **Find the y-intercept $b$:** Use point $(-2, 4)$: $$4 = \frac{7}{5} \times (-2) + b$$ $$4 = -\frac{14}{5} + b$$ Add $\frac{14}{5}$ to both sides: $$4 + \frac{14}{5} = b$$ Convert 4 to fraction with denominator 5: $$\frac{20}{5} + \frac{14}{5} = b$$ $$\frac{34}{5} = b$$ 5. **Write the final equation:** $$y = \frac{7}{5}x + \frac{34}{5}$$ This matches the approximate y-intercept near 6 and the positive slope.