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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:
This table presents x and y values for two linear functions to analyze and
compare their rates of change and y-
intercepts.
X
У
5
26
13
34
(1 point)
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.
O 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 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.
O 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.

1 answer

To compare Linear Function 1 and Linear Function 2 regarding their rates of change, we first analyze both functions.

  1. Linear Function 1: The equation is given as \( y = 15x + 8 \).

    • The rate of change (slope) can be identified directly from the equation: the coefficient of \( x \) is 15. So, the rate of change for Linear Function 1 is 15.

  2. Linear Function 2: We need to calculate the rate of change using the data provided in the table (which is not fully visible in the prompt). However, we can compute the rate of change using the points given:

    From the table:

    • When \( x = 5 \), \( y = 26 \)
    • When \( x = 13 \), \( y = 34 \)

    To find the rate of change (slope), we use the formula:
    \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the values:

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

    The calculation will be: \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]

Now, we can clearly see:

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

Thus, comparing the two:

  • Linear Function 1 has the greater rate of change.

Therefore, the correct statement is: 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.