1. **State the problem:** We are given four points representing average heart rate (y) at different running speeds (x): (8,140), (10,160), (12,180), and (14,200). We want to find the equation of the straight line that fits these points. 2. **Formula used:** The equation of a straight line is given by $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** The slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points (8,140) and (10,160): $$m = \frac{160 - 140}{10 - 8} = \frac{20}{2} = 10$$ Check with points (10,160) and (12,180): $$m = \frac{180 - 160}{12 - 10} = \frac{20}{2} = 10$$ Since the slope is consistent, $m=10$. 4. **Find the y-intercept $b$:** Use the equation $y = mx + b$ with one point, say (8,140): $$140 = 10 \times 8 + b$$ $$140 = 80 + b$$ $$b = 140 - 80 = 60$$ 5. **Final equation:** $$y = 10x + 60$$ This means the average heart rate increases by 10 bpm for every 1 km/hr increase in running speed, starting from 60 bpm at 0 km/hr. 6. **Summary:** The linear equation fitting the data points is $$y = 10x + 60$$ where $y$ is the average heart rate and $x$ is the running speed in km/hr.