To determine the slope of this function, we need to calculate the slope between each pair of points provided in the table. The slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's use the provided data points to calculate the slopes between consecutive pairs:
1. Calculate the slope between the points (2, 8.50) and (5, 15.25):
[tex]\[ m_1 = \frac{15.25 - 8.50}{5 - 2} = \frac{6.75}{3} = 2.25 \][/tex]
2. Calculate the slope between the points (5, 15.25) and (8, 22.00):
[tex]\[ m_2 = \frac{22.00 - 15.25}{8 - 5} = \frac{6.75}{3} = 2.25 \][/tex]
3. Calculate the slope between the points (8, 22.00) and (12, 31.00):
[tex]\[ m_3 = \frac{31.00 - 22.00}{12 - 8} = \frac{9.00}{4} = 2.25 \][/tex]
Since the slope is consistent and identical between all consecutive points, we conclude that the slope of this linear function is:
[tex]\[ \boxed{2.25} \][/tex]
Thus, the correct answer is 2.25.
