1. **Problem statement:** A local business's sales increased from 120 units at Week 0 to 195 units at Week 3. We need to find the sales growth rate (slope), predict sales at Week 7, and evaluate the manager's projection of 350 units. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ This represents the rate of change of sales per week. 3. **Calculate the slope:** Given points: $(0,120)$ and $(3,195)$ $$m=\frac{195 - 120}{3 - 0} = \frac{75}{3} = 25$$ So, sales increase by 25 units per week. 4. **Predict sales at Week 7:** Using the linear model $y = mx + b$, where $b$ is initial sales at Week 0: $$y = 25x + 120$$ At $x=7$: $$y = 25 \times 7 + 120 = 175 + 120 = 295$$ Predicted sales at Week 7 are 295 units. 5. **Evaluate the manager's projection:** The manager projects 350 units at Week 7, but our linear model predicts 295 units. Since 350 is higher than 295, the projection assumes a faster growth rate than the current trend. Unless there is new information or marketing efforts to increase sales growth, the projection seems optimistic and not supported by the current linear trend. **Final answers:** - Slope (growth rate) = 25 units/week - Predicted sales at Week 7 = 295 units - Manager's projection of 350 units is likely unreasonable based on current trend.