1. **State the problem:** Find the equation of the line passing through the points $(-2,1)$ and $(4,6)$. 2. **Formula used:** The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. The line equation in point-slope form is $y - y_1 = m(x - x_1)$. 3. **Calculate the slope:** $$m = \frac{6 - 1}{4 - (-2)} = \frac{5}{6}$$ 4. **Use point-slope form with point $(-2,1)$:** $$y - 1 = \frac{5}{6}(x - (-2)) = \frac{5}{6}(x + 2)$$ 5. **Simplify:** $$y - 1 = \frac{5}{6}x + \frac{5}{6} \times 2 = \frac{5}{6}x + \frac{10}{6}$$ 6. **Add 1 to both sides:** $$y = \frac{5}{6}x + \frac{10}{6} + 1$$ 7. **Convert 1 to sixths:** $$1 = \frac{6}{6}$$ 8. **Add fractions:** $$y = \frac{5}{6}x + \frac{10}{6} + \frac{6}{6} = \frac{5}{6}x + \frac{16}{6}$$ 9. **Simplify fraction:** $$\frac{16}{6} = \frac{8}{3}$$ **Final equation:** $$y = \frac{5}{6}x + \frac{8}{3}$$