Question
Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?Linear Function 1: y=15x+8Linear Function 2:x y5 2613 34(1 point)ResponsesLinear 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 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.
Answers
GPT-4o mini
To compare the rates of change of the two given linear functions, we first look at their forms.
**Linear Function 1:**
\[ y = 15x + 8 \]
- The rate of change (slope) for this function is **15**.
**Linear Function 2:**
The data for Linear Function 2 is given in the form of points: (5, 26), (13, 34). To find the rate of change, we can calculate the slope using the slope formula, which is
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points:
- \( (x_1, y_1) = (5, 26) \)
- \( (x_2, y_2) = (13, 34) \)
Now, applying the values:
\[ m = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
So the rate of change (slope) for Linear Function 2 is **1**.
**Comparison:**
- The rate of change for Linear Function 1 is **15**
- The rate of change for Linear Function 2 is **1**
Thus, **Linear Function 1 has the greater rate of change**.
**Final Answer:** 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:**
\[ y = 15x + 8 \]
- The rate of change (slope) for this function is **15**.
**Linear Function 2:**
The data for Linear Function 2 is given in the form of points: (5, 26), (13, 34). To find the rate of change, we can calculate the slope using the slope formula, which is
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points:
- \( (x_1, y_1) = (5, 26) \)
- \( (x_2, y_2) = (13, 34) \)
Now, applying the values:
\[ m = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
So the rate of change (slope) for Linear Function 2 is **1**.
**Comparison:**
- The rate of change for Linear Function 1 is **15**
- The rate of change for Linear Function 2 is **1**
Thus, **Linear Function 1 has the greater rate of change**.
**Final Answer:** 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.