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

Linear Function ? has the lesser rate of change.

Answer 1

To compare the rates of change of the two linear functions, we first need to determine the slope (rate of change) of each function.

**Linear Function 1** is given as:
\[ y = 7x + 4 \]
The rate of change (slope) is the coefficient of \(x\), which is \(7\).

**Linear Function 2** is represented by points (10, 61) and (12, 73). We can calculate the slope using 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:
- \((x_1, y_1) = (10, 61)\)
- \((x_2, y_2) = (12, 73)\)

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

Now we can compare the slopes:
- Rate of change for Linear Function 1: \(7\)
- Rate of change for Linear Function 2: \(6\)

Since \(6 < 7\), Linear Function 2 has the lesser rate of change.

Therefore, the answer is: **2**.