Question

Use the table to answer the question.

This table has the x and y values that will contribute to determining the rate of change and the initial value of the linear function.
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=−5
m equals negative 5

m=15
m equals 15

m=−15

Answer 1

To determine the rate of change (or slope \( m \)) of a linear function given two points \((x_1, y_1)\) and \((x_2, y_2)\), we can use the formula:

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

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

Now, substituting the values into the formula:

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

Calculating:

\[
m = \frac{9}{0.6} = 15
\]

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

\[
m = 15
\]

So the correct response is:

**m=15**