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.

(1 point)
Responses

m=−15
m equals negative 15

m=15
m equals 15

m=0.067
m equals 0.067

m=−5
m equals negative 5
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page 27 of 28

Answer 1

To determine the rate of change (slope) \( m \) of the linear function from the given table values, we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the values from the table:

• \( (x_1, y_1) = (2.6, -6) \)
• \( (x_2, y_2) = (3.2, 3) \)

Now, plug the values into the formula:

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

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

m = 15.