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 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 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: 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 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 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.
Answers
GPT-4o mini
To compare the rates of change of Linear Function 1 and Linear Function 2, let's analyze each function.
**Linear Function 1:**
The equation is given as \( y = 15x + 8 \). In this equation, the coefficient of \( x \) (which is \( 15 \)) represents the rate of change (or slope) of the linear function.
- Rate of change for Linear Function 1 = **15**
**Linear Function 2:**
We are provided with two points: (5, 26) and (13, 34). To find the rate of change (slope), we can use the slope formula given by:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (5, 26) as \((x_1, y_1)\) and (13, 34) as \((x_2, y_2)\), we plug in the values:
\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]
- Rate of change for Linear Function 2 = **1**
**Comparison:**
- **Linear Function 1:** Rate of change = 15
- **Linear Function 2:** Rate of change = 1
**Conclusion:**
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.
Thus, 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.**
**Linear Function 1:**
The equation is given as \( y = 15x + 8 \). In this equation, the coefficient of \( x \) (which is \( 15 \)) represents the rate of change (or slope) of the linear function.
- Rate of change for Linear Function 1 = **15**
**Linear Function 2:**
We are provided with two points: (5, 26) and (13, 34). To find the rate of change (slope), we can use the slope formula given by:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (5, 26) as \((x_1, y_1)\) and (13, 34) as \((x_2, y_2)\), we plug in the values:
\[
\text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1
\]
- Rate of change for Linear Function 2 = **1**
**Comparison:**
- **Linear Function 1:** Rate of change = 15
- **Linear Function 2:** Rate of change = 1
**Conclusion:**
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.
Thus, 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.**