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:
Values of x and y 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 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.

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 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 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.

Answer 1

To determine which linear function has the greater rate of change, we can analyze the given equations and values.

**Linear Function 1:**
This function is \( y = 15x + 8 \).
- The rate of change (slope) of a linear function in the form \( y = mx + b \) is given by \( m \).
- Thus, the rate of change for Linear Function 1 is \( 15 \).

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

Given points:
- When \( x = 5 \), \( y = 26 \) (point A: (5, 26))
- When \( x = 13 \), \( y = 34 \) (point B: (13, 34))

The rate of change (slope) between two points is calculated using the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the points:
\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]

Now we can compare the rates of change:

- Linear Function 1: rate of change = 15
- Linear Function 2: rate of change = 1

From the calculations:
- 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.

Therefore, 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.**