A coordinate plane shows the x-axis ranging from negative 6 to 18 in increments of 2 and the y-axis ranging from negative 2 to 26 in increments of 2. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 2 comma 16 right parenthesis and left parenthesis 6 comma 22 right parenthesis.

Question

Linear Function 2:
x
y

0 12
4 24
Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.

(1 point)
Linear Function
has the greater rate of change.
Remaining Attempts : 3
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Answer 1

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

For Linear Function 1: We are given two points: \( (2, 16) \) and \( (6, 22) \).

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the provided points into the formula: \[ m = \frac{22 - 16}{6 - 2} = \frac{6}{4} = \frac{3}{2} = 1.5 \]

So, the rate of change (slope) for Linear Function 1 is 1.5.

For Linear Function 2: We are given two points: \( (0, 12) \) and \( (4, 24) \).

Using the same slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points: \[ m = \frac{24 - 12}{4 - 0} = \frac{12}{4} = 3 \]

So, the rate of change (slope) for Linear Function 2 is 3.

Comparison:

• Linear Function 1 has a rate of change of 1.5.
• Linear Function 2 has a rate of change of 3.

Since 3 (Linear Function 2) is greater than 1.5 (Linear Function 1), the answer is:

Linear Function 2 has the greater rate of change.

So, the correct choice is: 2.