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 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. 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.

Answer 1

To compare the rates of change of Linear Function 1 and Linear Function 2, let's first identify the rate of change for each function.

**Linear Function 1** is given as:
\[ y = 15x + 8 \]
The coefficient of \( x \) (which is 15) represents the rate of change. Therefore, the rate of change for Linear Function 1 is 15.

**Linear Function 2** is represented by the table of \( x \) and \( y \) values:
- For \( x = 5 \), \( y = 26 \)
- For \( x = 13 \), \( y = 34 \)

To find the rate of change (slope) of Linear Function 2, we can use the formula for slope:
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \).

Calculating the change in \( y \) and \( x \):
\[
\Delta y = 34 - 26 = 8
\]
\[
\Delta x = 13 - 5 = 8
\]

Now calculate the rate of change:
\[
\text{slope} = \frac{8}{8} = 1
\]

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**.

Thus, Linear Function 1 has a greater rate of change compared to Linear Function 2.

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.**