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:
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 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.
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 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.

Answer 1

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

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

**Linear Function 2:**
To find the rate of change, we can calculate the slope using two points from the provided table:

- Point 1: (5, 26)
- Point 2: (13, 34)

The formula for the slope (rate of change) is given by:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values:
- \( y_1 = 26 \), \( y_2 = 34 \)
- \( x_1 = 5 \), \( x_2 = 13 \)

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

So, the rate of change for Linear Function 2 is **1**.

**Comparison:**
- Rate of change for Linear Function 1: **15**
- Rate of change for Linear Function 2: **1**

Since \( 15 > 1 \), we conclude that:

**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.**