Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?Linear Function 1: y=15x+8Linear Function 2:x y5 2613 34(1 point)ResponsesLinear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 8.Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 8.Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 15.Linear Function 2 has the greater rate of change, with a rate of change equal to 21 while Linear Function 1 has a rate of change equal to 15.Linear Function 1 has the greater rate of change, with a rate of change equal to 8 while Linear Function 2 has a rate of change equal to 1.Linear Function 1 has the greater rate of change, with a rate of change equal to 8 while Linear Function 2 has a rate of change equal to 1.Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.

1 answer

To compare the rates of change of the two given linear functions, we first look at their forms.

Linear Function 1: \[ y = 15x + 8 \]

  • The rate of change (slope) for this function is 15.

Linear Function 2: The data for Linear Function 2 is given in the form of points: (5, 26), (13, 34). To find the rate of change, we can calculate the slope using the slope formula, which is \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points:

  • \( (x_1, y_1) = (5, 26) \)
  • \( (x_2, y_2) = (13, 34) \)

Now, applying the values: \[ m = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]

So the rate of change (slope) for Linear Function 2 is 1.

Comparison:

  • The rate of change for Linear Function 1 is 15
  • The rate of change for Linear Function 2 is 1

Thus, Linear Function 1 has the greater rate of change.

Final Answer: Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.

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