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
y
=
7
x
+
4

Linear Function 2:
x
x
y
y

10 61
12 73
(1 point)

Answer 1

To determine which linear function has a lesser rate of change, we need to evaluate the slope of each function.

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

2. **Linear Function 2**:
To find the slope of Linear Function 2, we can use the two points provided: (10, 61) and (12, 73). The slope \( m \) is calculated using the formula:

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

Here, \( (x_1, y_1) = (10, 61) \) and \( (x_2, y_2) = (12, 73) \):

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

Now, we have the slopes:

- **Slope of Linear Function 1**: 7
- **Slope of Linear Function 2**: 6

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

**Answer**: 2