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

Answer 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 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 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.

Answer 2

To compare the rate of change of Linear Function 1 and Linear Function 2, we can analyze their slopes.

**Linear Function 1:**
The function is given as \( y = 15x + 8 \). The coefficient of \( x \) (which is 15) represents the rate of change (slope) of this linear function. Therefore, the rate of change for Linear Function 1 is **15**.

**Linear Function 2:**
For Linear Function 2, we have two data points:
- When \( x = 5 \), \( y = 26 \)
- When \( x = 13 \), \( y = 34 \)

To find the rate of change (slope) of this function, we can use the formula for slope, which is:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using our points:
- \( (x_1, y_1) = (5, 26) \)
- \( (x_2, y_2) = (13, 34) \)

Calculating the differences:
\[
\Delta y = 34 - 26 = 8
\]
\[
\Delta x = 13 - 5 = 8
\]

Now plug these values into the slope formula:
\[
\text{slope} = \frac{8}{8} = 1
\]

So, the rate of change for Linear Function 2 is **1**.

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

**Conclusion:**
Linear Function 1 has the greater rate of change.

Answer 3

Let's clarify the rates of change for both linear functions.

1. **Linear Function 1:** This function is given by the equation \( y = 15x + 8 \). The rate of change (slope) is 15.

2. **Linear Function 2:** We calculated its rate of change using the two points \( (5, 26) \) and \( (13, 34) \):
- The differences were calculated as follows:
- \( \Delta y = 34 - 26 = 8 \)
- \( \Delta x = 13 - 5 = 8 \)
- The slope (rate of change) is given by:
\[
\text{slope} = \frac{8}{8} = 1
\]

### Summary of Rates of Change:
- Linear Function 1: **15**
- Linear Function 2: **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.**

None of the other options you displayed are correct based on the calculations done. If you have any further questions or need additional clarification, feel free to ask!