Slope and y-intercepts Quick Check

Question

2 of 52 of 5 Items
Question
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=15
m equals 15

m=0.067
m equals 0.067

m=−5
m equals negative 5

m=−15
m equals negative 15
Skip to navigation

Answer 1

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

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

Using the values from the table:

• Point 1: \( (2.6, -6) \) → \( x_1 = 2.6, y_1 = -6 \)
• Point 2: \( (3.2, 3) \) → \( x_2 = 3.2, y_2 = 3 \)

Now, we can substitute the values into the formula:

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

Calculating the numerator and denominator:

1. \( y_2 - y_1 = 3 - (-6) = 3 + 6 = 9 \)
2. \( x_2 - x_1 = 3.2 - 2.6 = 0.6 \)

Now plug these values into the slope formula:

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

Calculating this:

\[ m = 15 \]

Thus, the rate of change (slope) of the linear function is:

m = 15.