Question

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

Answers

GPT-4o mini
To create an equation for the height of Dalvin's plant (HH) as a function of time (tt), we need some specifics about the graph itself (such as its slope and intercept). However, I can guide you through the general form you might expect based on common scenarios.

A linear relationship can typically be formatted as:

\[ HH = mt + b \]

Where:
- \( HH \) is the height of the plant in inches.
- \( t \) is the time in months since the plant was bought.
- \( m \) represents the rate of growth (the slope), or how many inches the plant grows per month.
- \( b \) is the \( y \)-intercept, which indicates the initial height of the plant at \( t = 0 \).

### Example Equation Interpretation
If the graph shows that the plant grows 2 inches per month, and the initial height of the plant when Dalvin bought it is 4 inches, the equation would be:

\[ HH = 2t + 4 \]

### Y-intercept Interpretation
The \( y \)-intercept (\( b \)) in this example is 4. This means that when \( t = 0 \) (the time when Dalvin bought the plant), the height of the plant was 4 inches.

### Final Confirmation
If you can provide specific data points, I can give you a more precise equation and interpretation.