1. **State the problem:** Find the equation of the line passing through the points $(-3, h(-3))$ and $(1, h(1))$ where $h(x) = x^3 + 2$. 2. **Calculate the points:** Calculate $h(-3)$: $$h(-3) = (-3)^3 + 2 = -27 + 2 = -25$$ Calculate $h(1)$: $$h(1) = 1^3 + 2 = 1 + 2 = 3$$ So the points are $(-3, -25)$ and $(1, 3)$. 3. **Find the slope $m$ of the line:** The slope formula is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Substitute the points: $$m = \frac{3 - (-25)}{1 - (-3)} = \frac{3 + 25}{1 + 3} = \frac{28}{4} = 7$$ 4. **Find the y-intercept $b$ using $y = mx + b$:** Use one point, for example $(-3, -25)$: $$-25 = 7 \times (-3) + b$$ $$-25 = -21 + b$$ Add 21 to both sides: $$-25 + 21 = b$$ $$\cancel{-25} + 21 = \cancel{-21} + b$$ $$-4 = b$$ 5. **Write the equation of the line:** $$y = 7x - 4$$ **Final answer:** The equation of the line passing through the points is $y = 7x - 4$.