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=−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 by the table, we can use the formula for the slope \( m \):

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

Using the values from the table:

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

Now substitute these 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 the values back into the slope formula:

\[ m = \frac{9}{0.6} \]

To simplify \( \frac{9}{0.6} \):

\[ m = 15 \]

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

\[ m = 15 \]

The correct response is:

m=15