1. **State the problem:** We need to find the linear equation relating price $x$ to sales $y$ given two points $(6, 3000)$ and $(8, 2000)$, then use it to predict sales at price $6.50$. 2. **Find the slope $m$ of the line:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2000 - 3000}{8 - 6} = \frac{-1000}{2} = -500$$ 3. **Use point-slope form to find the equation:** Using point $(6, 3000)$, $$y - 3000 = -500(x - 6)$$ 4. **Simplify the equation:** $$y - 3000 = -500x + 3000$$ $$y = -500x + 3000 + 3000$$ $$y = -500x + 6000$$ 5. **Predict sales at $x = 6.50$:** $$y = -500(6.50) + 6000 = -3250 + 6000 = 2750$$ **Final answers:** - Linear equation: $$y = -500x + 6000$$ - Predicted sales at price 6.50: $$2750$$