Question

there are 60 minutes in an hour. the total number of minutes is a function of the number of hours, as shown in the table. does this situation represent a linear or non-linear function, and why?

hours vs. minutes
hours | minutes
1 | 60
2 | 120
3 | 180
4 | 240
5 | 300

a it represents a linear function because there is a constant rate of change.
b it represents a linear function because there is not a constant rate of change.

Explanation:

⚡ Using what you learned: Rate of Change and Applications

Step 1: Calculate the rate of change

The rate of change is the change in minutes divided by the change in hours:

$$ \text{Rate of Change} = \frac{\text{Change in Minutes}}{\text{Change in Hours}} $$

Using the values from the table:

• From 1 to 2 hours:

$$ \frac{120 - 60}{2 - 1} = \frac{60}{1} = 60 $$

• From 2 to 3 hours:

$$ \frac{180 - 120}{3 - 2} = \frac{60}{1} = 60 $$

• From 3 to 4 hours:

$$ \frac{240 - 180}{4 - 3} = \frac{60}{1} = 60 $$

• From 4 to 5 hours:

$$ \frac{300 - 240}{5 - 4} = \frac{60}{1} = 60 $$

Step 2: Determine if the function is linear

A function is linear if it has a constant rate of change. Since the rate of change is constantly \(60\) minutes per hour, the function is linear.

Answer:

A It represents a linear function because there is a constant rate of change.