Annabelle bought a plant and planted it in a pot near a window in her house. Let HH represent the height of the plant, in inches, tt months since Annabelle bought the plant. A graph of HH is shown below. Write an equation for HH then state the slope of the graph and determine its interpretation in the context of the problem.

To solve this problem, we'll first consider the general form of a linear equation and then relate it to the context of the plant's height growth over time.

### Step 1: Identify the General Form of a Linear Equation

The height \( H \) of the plant as a function of time \( t \) months can be represented by a linear equation of the form:

\[
H = mt + b
\]

where:
- \( m \) is the slope of the line, representing the rate of change of the plant's height per month.
- \( b \) is the y-intercept, representing the initial height of the plant at the time when \( t = 0 \) (when Annabelle first bought the plant).

### Step 2: Determine the Slope (m) and its Interpretation

To determine the slope \( m \), we need to analyze the rate at which the height of the plant changes over time. The slope is calculated as:

\[
m = \frac{\Delta H}{\Delta t}
\]

where:
- \( \Delta H \) is the change in height.
- \( \Delta t \) is the change in time (in months).

### Step 3: Interpretation in Context

The slope \( m \) represents the growth rate of the plant in inches per month. If the slope is positive, it means the plant is growing, and the specific value of \( m \) will tell us how many inches the plant grows each month.

To fully determine the equation and the slope's value, we need either a graph or specific points from the graph that show how the height changes over time. Could you provide more details or describe the graph?

Annabelle bought a plant and planted it in a pot near a window in her house. Let H represent the height of the plant, in inches, t months since Annabelle bought the plant. A graph of H is shown below. Write an equation for H, then state the slope of the graph and determine its interpretation in the context of the problem.

Solve a linear equation problem where Annabelle tracks the growth of her plant over time. Learn how to calculate the slope (rate of growth) and interpret its meaning in inches per month. This problem is suitable for students in Grades 8-10, covering linear equations and rate of change.

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