Question

Question was provided via image upload.

Explanation:

Identify key points on the linear graph

$$
LATEXBLOCK0
$$

Calculate the slope (rate of change)

$$
LATEXBLOCK1
$$

Determine the linear equation

$$
LATEXBLOCK2
$$

Answer:

The linear relationship representing Duke's weight over time is:

$$y = 2.5x + 15$$

Where:

• \(y\) represents Duke's weight in pounds.
• \(x\) represents the number of weeks since adoption.
• The initial weight at adoption (\(y\)-intercept) is \(15\text{ pounds}\).
• The rate of growth (slope) is \(2.5\text{ pounds per week}\).