Slope and y-intercepts Quick Check

Question

2 of 52 of 5 Items
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=−15
m equals negative 15

m=15
m equals 15

m=0.067
m equals 0.067

m=−5

Answer 1

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

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

From the table provided, we have the points:

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

Now, we can 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, substituting back into the slope formula:

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

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

\[ m = 15 \]

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

m = 15