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Question

Linear Function 1:
A coordinate plane shows the x-axis ranging from negative 1 to 4 in increments of 1 and the y-axis ranging from negative 1 to 13 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 1 comma 9 right parenthesis and left parenthesis 2 comma 12 right parenthesis.

Linear Function 2:
x
y
0 2
5 42
Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?

(1 point)
Responses

Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.

Linear Function 1 has the greater rate of change, with a rate of change equal to 3 while Linear Function 2 has a rate of change equal to 2.
Linear Function 1 has the greater rate of change, with a rate of change equal to 3 while Linear Function 2 has a rate of change equal to 2.

Linear Function 1 has the greater rate of change, with a rate of change equal to 6 while Linear Function 2 has a rate of change equal to 2.
Linear Function 1 has the greater rate of change, with a rate of change equal to 6 while Linear Function 2 has a rate of change equal to 2.

Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 6.
Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 6.
Remaining Attempts : 3
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Answer 1

To compare the rates of change for Linear Function 1 and Linear Function 2, we will calculate the rate of change (slope) for each function.

For Linear Function 1:

• The two points provided are (1, 9) and (2, 12).
• The formula for the rate of change (slope) between two points (x₁, y₁) and (x₂, y₂) is: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
• Applying the values: \[ \text{slope for Linear Function 1} = \frac{12 - 9}{2 - 1} = \frac{3}{1} = 3 \]

For Linear Function 2:

• The two points provided are (0, 2) and (5, 42).
• Using the same slope formula: \[ \text{slope for Linear Function 2} = \frac{42 - 2}{5 - 0} = \frac{40}{5} = 8 \]

Comparison:

• Linear Function 1 has a rate of change of 3.
• Linear Function 2 has a rate of change of 8.

Thus, Linear Function 2 has the greater rate of change.

The correct response is: "Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3."