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 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.

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 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 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.

1 answer

To compare the rates of change of the two linear functions, we need to identify the rate of change, which is represented by the coefficient of \(x\) in the equation of a linear function or can be calculated using points for a function given in a table.

Linear Function 1:

The function is given as: \[ y = 15x + 8 \] Here, the coefficient of \(x\) is \(15\). Therefore, the rate of change for Linear Function 1 is \(15\).

Linear Function 2:

We have two points:

  • \( (5, 26) \)
  • \( (13, 34) \)

We can find the rate of change (slope) by using the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the points:

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

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

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

Comparison

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

Conclusion

Linear Function 1 has the greater rate of change.

Final Response: 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.