1. **State the problem:** Find the equation of the secant line passing through the points $(-3, g(-3))$ and $(5, g(5))$ on the curve defined by $g(x) = x^2 - 9x$. 2. **Find the coordinates of the points:** Calculate $g(-3)$: $$g(-3) = (-3)^2 - 9(-3) = 9 + 27 = 36$$ Calculate $g(5)$: $$g(5) = 5^2 - 9(5) = 25 - 45 = -20$$ So the points are $(-3, 36)$ and $(5, -20)$. 3. **Find the slope $m$ of the secant line:** Use the slope formula: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-20 - 36}{5 - (-3)} = \frac{-56}{8}$$ Show cancellation: $$m = \frac{\cancel{-56}}{\cancel{8}} = -7$$ 4. **Find the equation of the line $y = mx + b$:** Use point-slope form with point $(-3, 36)$: $$36 = -7(-3) + b$$ Simplify: $$36 = 21 + b$$ Solve for $b$: $$b = 36 - 21 = 15$$ 5. **Write the final equation:** $$y = -7x + 15$$ This is the equation of the secant line passing through the given points on the curve $g(x) = x^2 - 9x$.