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To determine the number of inches the plant grows per month, we need to find the rate of change, or the slope, between the values of \( t \) (months) and \( H \) (height in inches).

In a linear relationship, the slope \( m \) between two points \((t_1, H_1)\) and \((t_2, H_2)\) is calculated by:
\[
m = \frac{H_2 - H_1}{t_2 - t_1}
\]

### Step-by-Step Solution

Let's use two pairs of values from the table to calculate this rate of growth:

1. Using \((t_1, H_1) = (4.5, 34.5)\) and \((t_2, H_2) = (7, 47)\):
   \[
   m = \frac{47 - 34.5}{7 - 4.5} = \frac{12.5}{2.5} = 5 \text{ inches per month}
   \]

2. We can check the consistency of this growth rate with another pair, say, \((t_1, H_1) = (7, 47)\) and \((t_2, H_2) = (9, 57)\):
   \[
   m = \frac{57 - 47}{9 - 7} = \frac{10}{2} = 5 \text{ inches per month}
   \]

Both pairs give the same rate of growth, confirming that the plant grows at a constant rate of **5 inches per month**.

### Final Answer
The number of inches the plant grows per month is **5 inches**.

Would you like further details or have any questions?

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Here are some related questions for practice:
1. If the plant started at 20 inches tall, what would its height be after 10 months?
2. How tall will the plant be at 15 months, assuming the same growth rate?
3. If the growth rate changed to 3 inches per month, how would that affect the height at \( t = 9 \)?
4. What would the value of \( t \) be when \( H = 72 \) inches?
5. How would you represent this linear relationship in equation form?

**Tip:** In linear functions, the slope (rate of change) tells you how much the dependent variable changes for each unit increase in the independent variable.

William bought a plant and planted it in a pot near a window in his house. Let H represent the height of the plant, in inches, t months since William bought the plant. The table below has select values showing the linear relationship between t and H. Determine the number of inches the plant grows per month.

Learn how to determine the growth rate of a plant given a linear relationship between time in months (t) and height in inches (H). Using values from a table, calculate the plant’s monthly growth rate with the slope formula. Suitable for middle school students (Grades 6-8).

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