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 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 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 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 of the two linear functions, we need to analyze the slope of each function.

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

2. **Linear Function 2**:
- We don't have the equation but have the data from a table of points.
- Given points:
- For \( x = 5 \), \( y = 26 \)
- For \( x = 13 \), \( y = 34 \)
- To find the rate of change, we use the formula for slope:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
- Here, \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \):
\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]

Now we have:

- **Linear Function 1**: Rate of change = 15
- **Linear Function 2**: Rate of change = 1

**Comparison**:
- Linear Function 1 has a greater rate of change (15) compared to Linear Function 2 (1).

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.**