Question

Question
Use the table to answer the question.

Rate of Change and Initial Value from x and y Values
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=0.067
m equals 0.067

m=15
m equals 15

m=−5
m equals negative 5

m=−15

Answer 1

To determine the rate of change (slope) of the linear function given by the table of values, we can use the formula for the slope \( m \):

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

From the table, we have the following points:
- \( (x_1, y_1) = (2.6, -6) \)
- \( (x_2, y_2) = (3.2, 3) \)

Now, we can plug the values into the 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, substituting these values back to find \( m \):

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

Now performing the division:

\[
m = 15
\]

So, the rate of change is:

\[
\boxed{15}
\]

The correct response is:
- \( m = 15 \)
- \( m \) equals 15