Question

Compare Linear Function 1 with Linear Function 2. Which one has the lesser rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.Linear Function 1: y=7x+4 Linear Function 2: x y 10 6112 73(1 point)Linear Function has the lesser rate

Answer 1

To compare the rates of change of the two linear functions, we can analyze their slopes.

1. **Linear Function 1:** \( y = 7x + 4 \)
- The slope (rate of change) is 7.

2. **Linear Function 2:** To determine the slope from the given points (10, 6) and (12, 7), we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the values:
- \( (x_1, y_1) = (10, 6) \)
- \( (x_2, y_2) = (12, 7) \)
\[
\text{slope} = \frac{7 - 6}{12 - 10} = \frac{1}{2} = 0.5
\]

Now we can compare the slopes:
- Slope of Linear Function 1: 7
- Slope of Linear Function 2: 0.5

Since 0.5 is less than 7, **Linear Function 2** has the lesser rate of change.

**Final answer: 2** (Linear Function 2 has the lesser rate of change).