Use the table to answer the question.

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=−15
m equals negative 15

m=15
m equals 15

m=−5

Answer 1

To determine the rate of change (slope, \( m \)) of the linear function from the given \( (x, y) \) values, we can use the formula for the slope between two points:

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

Given the points \( (2.6, -6) \) and \( (3.2, 3) \):

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

Now we can plug in 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:

\[ 3.2 - 2.6 = 0.6 \]

Putting it all together:

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

Calculating that:

\[ m = 15 \]

So, the rate of change of the linear function is \( m = 15 \).

Thus, the correct response is:

m = 15.