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Linear Function 1:
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.

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.

1 answer

To determine which linear function has the greater rate of change, we need to calculate the slope (rate of change) for each function.

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

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

Using the points:

  • \( x_1 = 2, y_1 = 16 \)
  • \( x_2 = 6, y_2 = 22 \)

Calculating the slope: \[ m_1 = \frac{22 - 16}{6 - 2} = \frac{6}{4} = \frac{3}{2} \]

For Linear Function 2: We have the points (0, 12) and (4, 24).

Using the slope formula:

  • \( x_1 = 0, y_1 = 12 \)
  • \( x_2 = 4, y_2 = 24 \)

Calculating the slope: \[ m_2 = \frac{24 - 12}{4 - 0} = \frac{12}{4} = 3 \]

Comparison:

  • Rate of change for Linear Function 1: \( \frac{3}{2} = 1.5 \)
  • Rate of change for Linear Function 2: \( 3 \)

Since \( 3 > 1.5 \), Linear Function 2 has the greater rate of change.

Final Answer: Linear Function 2 has the greater rate of change.