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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:
Applying the information provided to analyze and compare the rate of change between two linear functions.
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 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.

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.
Remaining Attempts : 3
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1 answer

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

Linear Function 1:

  • We are given two points: (1, 9) and (2, 12).

  • The formula for the slope (rate of change) is:

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

    Applying the coordinates:

    \[ m_1 = \frac{12 - 9}{2 - 1} = \frac{3}{1} = 3 \]

Linear Function 2:

  • We are given two points: (0, 2) and (5, 42).

  • Using the same slope formula:

    \[ m_2 = \frac{42 - 2}{5 - 0} = \frac{40}{5} = 8 \]

Now we can compare the rates of change of both functions:

  • Rate of change for Linear Function 1 is 3.
  • Rate of change for Linear Function 2 is 8.

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

Thus, 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.