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:
Analyzing the provided values to determine which linear function has the lower rate of change.
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 rate of change for both functions.

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

**Linear Function 2:**
To find the rate of change (slope), we need to use 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:

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

Plugging in the values:

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

We calculate as follows:

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

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

**Comparison:**
Since 6 (from Linear Function 2) is less than 7 (from Linear Function 1), Linear Function 2 has the lesser rate of change.

**Conclusion:**
Linear Function 2 has the lesser rate of change. Therefore, the answer is:

**2**