Question

Properties of Functions Quick Check
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Question
Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?

Linear Function 1: y=15x+8

Linear Function 2:
This table presents x and y values for two linear functions to analyze and compare their rates of change and y-intercepts.
x
y

5 26
13 34
(1 point)
Responses

Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 15.
Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 15.

Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.
Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.

Linear Function 1 has the greater rate of change, with a rate of change equal to 8 while Linear Function 2 has a rate of change equal to 1.
Linear Function 1 has the greater rate of change, with a rate of change equal to 8 while Linear Function 2 has a rate of change equal to 1.

Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 8.
Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 8.

Answer 1

To compare the rates of change of the two linear functions, we need to analyze them individually.

1. **Linear Function 1:** \( y = 15x + 8 \)
- The rate of change (slope) of this function is 15.

2. **Linear Function 2:** We need to calculate the rate of change based on the provided table of values.

Given:
- For \( x = 5 \), \( y = 26 \)
- For \( x = 13 \), \( y = 34 \)

To find the rate of change, we can use the formula for slope:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values from the table:
\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]

Now we can compare the rates of change:
- Linear Function 1 has a rate of change of 15.
- Linear Function 2 has a rate of change of 1.

So, Linear Function 1 has the greater rate of change.

The correct response is:
**Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.**