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 61
12 73
(1 point)
Linear Function
has the lesser rate of change.

Answer 1

To determine which linear function has the lesser rate of change, we need to find the slope (rate of change) of each function.

1. **Linear Function 1**: The equation is \(y = 7x + 4\). The coefficient of \(x\) (which is 7) represents the slope. So, the rate of change for Linear Function 1 is **7**.

2. **Linear Function 2**: We have the points (10, 61) and (12, 73). To find the slope (rate of change), we use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values:
\[
\text{slope} = \frac{73 - 61}{12 - 10} = \frac{12}{2} = 6
\]
So, the rate of change for Linear Function 2 is **6**.

Now, we compare the rates of change:
- Linear Function 1 has a rate of change of **7**.
- Linear Function 2 has a rate of change of **6**.

Therefore, **Linear Function 2** has the lesser rate of change.

**Linear Function 2** has the lesser rate of change.