To determine the rate of change (slope) of the linear function represented by the two points in the table, we can use the formula for the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
From the table, we have the points:
- \( (x_1, y_1) = (2.6, -6) \)
- \( (x_2, y_2) = (3.2, 3) \)
Now, substituting the values into the slope formula:
\[ m = \frac{3 - (-6)}{3.2 - 2.6} \]
Calculating the numerator:
\[ 3 - (-6) = 3 + 6 = 9 \]
Calculating the denominator:
\[ 3.2 - 2.6 = 0.6 \]
Now, substitute these values back into the slope formula:
\[ m = \frac{9}{0.6} \]
To simplify \( \frac{9}{0.6} \):
\[ \frac{9}{0.6} = 15 \]
Therefore, the rate of change of the linear function is:
m = 15