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
=

5
m equals negative 5

m=−15
m
=

15
m equals negative 15

m=15
m
=
15
m equals 15

m=0.067
m
=
0.067
m equals 0.067

1 answer

To determine the rate of change (slope) of the linear function represented by the two points in the table, we can use the formula for the slope \( m \):

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

Given the two points from the table:

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

Now we can substitute the values into the slope formula:

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

Calculating the numerator:

\[ 3 - (-6) = 3 + 6 = 9 \]

And calculating the denominator:

\[ 3.2 - 2.6 = 0.6 \]

Now substituting these values back into the slope formula:

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

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

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

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

\[ m = 15 \]

So the correct response is:

m = 15.