To find the rate of change in the purchase price of broccoli in dollars per pound, we can calculate the slope of the line that passes through the given points \((3, 8.25)\) and \((6, 16.50)\).
The formula for the slope (or rate of change) \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For the points \((3, 8.25)\) and \((6, 16.50)\):
- \( (x_1, y_1) = (3, 8.25) \)
- \( (x_2, y_2) = (6, 16.50) \)
Now, plug these values into the slope formula:
\[ m = \frac{16.50 - 8.25}{6 - 3} \]
Calculating the numerator:
\[ 16.50 - 8.25 = 8.25 \]
Calculating the denominator:
\[ 6 - 3 = 3 \]
Now, substituting back into the formula gives:
\[ m = \frac{8.25}{3} = 2.75 \]
Thus, the rate of change in the purchase price of broccoli is $2.75 per pound.