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 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 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.

Answer 1

To compare the rates of change of the two linear functions, we first identify the slope (rate of change) of each function.

**Linear Function 1** is given in slope-intercept form:
\[ y = 15x + 8 \]
The slope (rate of change) here is 15.

**Linear Function 2** is represented by points (5, 26) and (13, 34). We can calculate the slope using the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Let \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \):
\[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]

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

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