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 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 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.
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Answer 1

To compare the two linear functions in terms of their rates of change, we can extract the slopes from their respective equations and data.

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

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

To find the rate of change for Linear Function 2, we can use the formula for the slope between two points:
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the values from Linear Function 2:
- Let \( (x_1, y_1) = (5, 26) \)
- Let \( (x_2, y_2) = (13, 34) \)

Now substitute these values into the formula:
\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]

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

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

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.**