1. **State the problem:** We are given two points representing the number of employees (in millions) in educational services for years 2005 and 2014, with $x=5$ for 2005 and $x=14$ for 2014. The points are $(5, 12.6)$ and $(14, 19.7)$. We need to find the linear equation modeling this data and estimate the number of employees in 2013, which corresponds to $x=13$. 2. **Formula used:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{19.7 - 12.6}{14 - 5} = \frac{7.1}{9} \approx 0.79$$ 4. **Find the y-intercept $b$:** Use one point, say $(5, 12.6)$: $$12.6 = 0.79 \times 5 + b \implies b = 12.6 - 3.95 = 8.65$$ 5. **Write the linear equation:** $$y = 0.79x + 8.65$$ 6. **Estimate the number of employees in 2013 ($x=13$):** $$y = 0.79 \times 13 + 8.65 = 10.27 + 8.65 = 18.92$$ **Final answers:** - Linear equation: $$y = 0.79x + 8.65$$ - Estimated employees in 2013: $$18.92$$ million