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 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.

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.

Answer 1

To compare the rates of change of the two linear functions, we need to analyze each function.

**Linear Function 1:**
Given as \( y = 15x + 8 \), the rate of change (slope) is 15.

**Linear Function 2:**
The table provides x and y values. We can calculate the rate of change by using two points from the table. Let’s use the points (5, 26) and (13, 34).

The formula for the rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the two points:
- \( (x_1, y_1) = (5, 26) \)
- \( (x_2, y_2) = (13, 34) \)

Calculating the slope:
\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]

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

**Conclusion:**
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.

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.**