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 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. 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 (slopes) of Linear Function 1 and Linear Function 2, we can analyze each function:

**Linear Function 1:**
The function is given as \( y = 15x + 8 \). The rate of change (slope) is the coefficient of \( x \), which is \( 15 \).

**Linear Function 2:**
This function is presented as a set of points: (5, 26) and (13, 34). To find the rate of change, we can use the slope formula:

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

Plugging in the given points, where \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \):

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

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 \( 1 \).

Therefore, **Linear Function 1 has the greater rate of change**.

Correct response:
**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.**