Question

Properties of Functions Quick Check 1 of 51 of 5 Items 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 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 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 first need to identify the rate of change for each function.

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

**Linear Function 2**:
We are provided with a table of values. Let's calculate the rate of change (slope) from the given points in the table. The x and y values provided are:

- \( (5, 26) \)
- \( (13, 34) \)

To find the slope (rate of change), we can use the formula:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the values from the table:

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

Now we can summarize the rates of change:
- **Linear Function 1**: rate of change = 15
- **Linear Function 2**: rate of change = 1

Now, we can compare the two rates of change:
- Linear Function 1 has a greater rate of change (15) compared to Linear Function 2 (1).

Based on the options provided, 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.**