the table below represents a linear function. identify the rate of change of the function.

Explanation:

Step1: Recall the formula for rate of change (slope)

The formula for the slope (m) between two points ((x_1,y_1)) and ((x_2,y_2)) is (m=\frac{y_2 - y_1}{x_2 - x_1}).

Step2: Select two points from the table

Let's take ((x_1,y_1)=(0,-4)) and ((x_2,y_2)=(4,1)).

Step3: Substitute into the formula

(m=\frac{1-(-4)}{4 - 0}=\frac{1 + 4}{4}=\frac{5}{4}). We can check with another pair of points, say ((x_1,y_1)=(4,1)) and ((x_2,y_2)=(8,6)). (m=\frac{6 - 1}{8 - 4}=\frac{5}{4}). Another check with ((x_1,y_1)=(8,6)) and ((x_2,y_2)=(12,11)) (m=\frac{11 - 6}{12 - 8}=\frac{5}{4}).

Answer:

(\frac{5}{4})