Subjects algebra

Rate Of Change 3A0247

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

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.