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 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.

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 determine which linear function has the greater rate of change, we first need to analyze both functions.

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

**Linear Function 2:**
To find the rate of change for Linear Function 2 from the given points, we can use the formula for the slope, which is:

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

Using the points (5, 26) and (13, 34):

- \( (x_1, y_1) = (5, 26) \)
- \( (x_2, y_2) = (13, 34) \)

Now, plugging in these values:

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

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

**Comparison:**

- The rate of change for Linear Function 1 is 15.
- The rate of change for Linear Function 2 is 1.

Thus, **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.**

Therefore, 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.**