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 first need to identify the rates of change of both functions.

**Linear Function 1:**
\( y = 7x + 4 \)

The rate of change (slope) is the coefficient of \( x \), which is **7**.

**Linear Function 2:**
We need to calculate the rate of change between the given points (10, 61) and (12, 73). The formula for the rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using the points (10, 61) and (12, 73):

- \(x_1 = 10\), \(y_1 = 61\)
- \(x_2 = 12\), \(y_2 = 73\)

Calculating the slope:

\[
\text{slope} = \frac{73 - 61}{12 - 10} = \frac{12}{2} = 6
\]

Now we can compare the rates of change:

- **Linear Function 1 Rate of Change:** 7
- **Linear Function 2 Rate of Change:** 6

Since 6 < 7, **Linear Function 2** has the lesser rate of change.

So the answer is:

**2**