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.
Remaining Attempts : 3

Answer 1

To determine which linear function has a lesser rate of change, we need to analyze both functions.

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

The rate of change for this function is given directly by the coefficient of \( x \), which is \( 7 \).

2. **Linear Function 2:** We need to find the rate of change based on the provided points.

From the points (10, 61) and (12, 73), we can calculate the slope (rate of change) using the formula for slope \( m \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
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 compare the rates of change:
- 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.

Thus, the answer is:

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