1. The problem involves understanding the relationship between the trunk diameter (in cm) and the age (in years) of two types of trees: Eastern hemlock and Giant redwood, as shown in the graph. 2. The graph shows two data series: Eastern hemlock with a roughly linear increase in age as trunk diameter increases, reaching about 400 years at 200 cm diameter, and Giant redwood with a slower increase, reaching just above 150 years at 200 cm diameter. 3. To model these relationships, we use the linear equation formula: $$y = mx + b$$ where $y$ is the age, $x$ is the trunk diameter, $m$ is the slope (rate of age increase per cm), and $b$ is the y-intercept (age when diameter is zero). 4. For Eastern hemlock: - At $x=0$, $y=0$ (assuming no age at zero diameter), so $b=0$. - At $x=200$, $y=400$. - Slope $m = \frac{400 - 0}{200 - 0} = 2$. - Equation: $$y = 2x$$. 5. For Giant redwood: - At $x=0$, $y=0$, so $b=0$. - At $x=200$, $y \approx 150$. - Slope $m = \frac{150 - 0}{200 - 0} = 0.75$. - Equation: $$y = 0.75x$$. 6. These linear models explain how age increases with trunk diameter for each tree type. 7. In summary: - Eastern hemlock age: $$y = 2x$$ - Giant redwood age: $$y = 0.75x$$ This means Eastern hemlock ages faster relative to trunk diameter than Giant redwood.