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 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 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 15.
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 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 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 15.
Answers
GPT-4o mini
To compare the rates of change for the two linear functions, we start with Linear Function 1 and then find the rate of change for Linear Function 2 from the provided data.
### Linear Function 1:
The function is given in slope-intercept form \( y = 15x + 8 \).
- The rate of change (slope) is the coefficient of \( x \), which is **15**.
### Linear Function 2:
We need to determine the rate of change from the provided table. The table has the following data points:
- When \( x = 5 \), \( y = 26 \)
- When \( x = 13 \), \( y = 34 \)
To find the rate of change (slope), we can use the formula:
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (5, 26) \) and \( (13, 34) \):
- \( y_1 = 26 \), \( y_2 = 34 \)
- \( x_1 = 5 \), \( x_2 = 13 \)
Now plug in the values:
\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]
### Summary of Rates of Change:
- Linear Function 1 has a rate of change of **15**.
- Linear Function 2 has a rate of change of **1**.
### Conclusion:
Linear Function 1 has the greater rate of change, which is **15**, compared to Linear Function 2’s rate of change of **1**.
So the correct response would be:
**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:
The function is given in slope-intercept form \( y = 15x + 8 \).
- The rate of change (slope) is the coefficient of \( x \), which is **15**.
### Linear Function 2:
We need to determine the rate of change from the provided table. The table has the following data points:
- When \( x = 5 \), \( y = 26 \)
- When \( x = 13 \), \( y = 34 \)
To find the rate of change (slope), we can use the formula:
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (5, 26) \) and \( (13, 34) \):
- \( y_1 = 26 \), \( y_2 = 34 \)
- \( x_1 = 5 \), \( x_2 = 13 \)
Now plug in the values:
\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]
### Summary of Rates of Change:
- Linear Function 1 has a rate of change of **15**.
- Linear Function 2 has a rate of change of **1**.
### Conclusion:
Linear Function 1 has the greater rate of change, which is **15**, compared to Linear Function 2’s rate of change of **1**.
So the correct response would be:
**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.**