1. **State the problem:** We are given two points representing profits after certain years: (1, 3) and (4, 15), where $x$ is years in business and $y$ is profit in millions. We need to find the linear equation $y=mx+b$, interpret slope and intercept, estimate profit at year 10, and find the year when profit reaches 70 million. 2. **Find the slope $m$:** The slope formula is $$m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{15 - 3}{4 - 1} = \frac{12}{3} = 4.$$ This means profit increases by 4 million per year. 3. **Find the y-intercept $b$:** Use point-slope form with point (1,3): $$y = mx + b \Rightarrow 3 = 4 \times 1 + b \Rightarrow b = 3 - 4 = -1.$$ So the equation is $$y = 4x - 1.$$ The y-intercept is -1 million, meaning at year 0 (before business started), profit would be -1 million (a conceptual starting point). 4. **Interpret slope and intercept:** - Slope 4 means profit increases by 4 million each year. - Y-intercept -1 means the model predicts a loss of 1 million at year 0. 5. **Estimate profit at year 10:** Substitute $x=10$ into the equation: $$y = 4(10) - 1 = 40 - 1 = 39.$$ So profit is estimated at 39 million after 10 years. 6. **Find year when profit is 70 million:** Set $y=70$ and solve for $x$: $$70 = 4x - 1 \Rightarrow 70 + 1 = 4x \Rightarrow 71 = 4x \Rightarrow x = \frac{71}{4} = 17.75.$$ So profit reaches 70 million during the 18th year. Final answers: - Equation: $$y = 4x - 1$$ - Slope meaning: profit increases 4 million per year - Y-intercept meaning: profit was -1 million at year 0 - Profit at year 10: 39 million - Year profit reaches 70 million: year 17.75 (about 18th year)