Use the table to answer the question.

Question

x
y
2.6 −6
3.2 3
Determine the rate of change of the linear function given as a table of values.
m=−5
m equals negative 5

m=−15
m equals negative 15

m=0.067
m equals 0.067

m=15

Answer 1

To determine the rate of change (slope) of the linear function represented in the table, we can use the formula for 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, substitute these values into the slope formula:

\[ m = \frac{3 - (-6)}{3.2 - 2.6} \] \[ m = \frac{3 + 6}{3.2 - 2.6} \] \[ m = \frac{9}{0.6} \] \[ m = 15 \]

Therefore, the rate of change of the linear function is:

m = 15.