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 need to compare the slopes of the two functions.

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

**For Linear Function 2:**
To find the slope from the provided points, we can use the two points given: (10, 61) and (12, 73).

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Plugging in the points:
- \( (x_1, y_1) = (10, 61) \)
- \( (x_2, y_2) = (12, 73) \)

Calculating:

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

Now we can compare the rates of change:

- Linear Function 1 has a rate of change of \( 7 \).
- Linear Function 2 has a rate of change of \( 6 \).

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.