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?

Answer 1

Answer:

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

Step-by-step explanation:

Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.

Here, number of hours represents input value and minutes represents the output value,

Now, By the given table,

The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),

Also,

$\frac{120-60}{2-1}=\frac{180-120}{3-2}=\frac{240-180}{4-3}=\frac{300-240}{5-4}=60$

⇒  The rate of change output value with respect to input value remains constant,

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

Answer 2

The first one I think because a linear function is always going to have a constant rate of change in one direction going straight up