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Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?

Linear Function 1: y=15x+8
Linear Function 2:
x
y
5 26
13 34
(1 point)
Responses

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 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.
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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1 answer

To compare the rates of change of the two linear functions, we need to analyze their equations and data points.

Linear Function 1: The equation is given as \( y = 15x + 8 \).
The rate of change (slope) of this function is the coefficient of \( x \), which is 15.

Linear Function 2: We have two points provided:

  1. \( (5, 26) \)
  2. \( (13, 34) \)

To find the rate of change (slope) for Linear Function 2, we use the formula for slope:

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

Substituting the points:

\[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]

Comparison of Rates of Change:

  • Linear Function 1 has a rate of change of 15.
  • Linear Function 2 has a rate of change of 1.

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

Correct 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.