1. **State the problem:** Find the equation of the line passing through the points $(-9, 3)$ and $(-3, 7)$ in slope-intercept form $y=mx+b$. 2. **Formula for slope:** The slope $m$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. 3. **Calculate the slope:** Using points $(-9,3)$ and $(-3,7)$, $$m=\frac{7 - 3}{-3 - (-9)}=\frac{4}{6}=\frac{2}{3}$$ 4. **Use point-slope form:** The equation is $$y - y_1 = m(x - x_1)$$ Using point $(-9,3)$, $$y - 3 = \frac{2}{3}(x + 9)$$ 5. **Simplify to slope-intercept form:** $$y - 3 = \frac{2}{3}x + 6$$ Add 3 to both sides: $$y = \frac{2}{3}x + 9$$ 6. **Verify with another point:** Check point $(-3,7)$: $$y = \frac{2}{3}(-3) + 9 = -2 + 9 = 7$$ which matches the point. **Final answer:** $$y = \frac{2}{3}x + 9$$