1. The problem asks to describe the rate of change of the height of a tomato plant over time, given a linear graph.
2. The rate of change in a linear relationship is the slope of the line, calculated by the formula:
$$\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$
where $y$ represents height and $x$ represents time.
3. From the graph, approximate two points on the line: $(2, 5)$ and $(16, 16)$.
4. Calculate the slope:
$$\text{slope} = \frac{16 - 5}{16 - 2} = \frac{11}{14}$$
5. Simplify the fraction:
$$\text{slope} = \frac{11}{14}$$ (already in simplest form)
6. This means the height of the tomato plant increases by $\frac{11}{14}$ centimeters per day.
7. In plain language: The height of the tomato plant grows approximately $0.79$ centimeters each day.
Final answer: The height of the tomato plant increases by $\frac{11}{14}$ centimeters per day.
Rate Of Change 3A0247
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