Question

Use the table to answer the 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**