Question

The table below represents the number of math problems Jana completed as a function of the number of minutes since she began doing her homework. Does this situation represent a linear or non-linear function, and why?

minutes math problems completed
__________________________________________
1 -3
2 -7
3 -12
4 -16
5 -19

Answer 1

It's a nonlinear because the x and y values are not increasing at the same ratio each time. This would be an example of a linear function:
x l 1 2 3 4 5 6
y l 3 6 9 12 15 18

As x increases by 1, y increases by a multiple of 3

Answer 2

Given function is not a linear function as rate of change varies for different pairs of points.

Explanation:

We are given the table,

x f(x)

1 -3

2 -7

3 -12

4 -16

5 -19

To check whether the given function is linear, we will check the rate of change at different points.

As, the rate of change of
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is given by,
`(y_(2)-y_(1))/(x_(2)-x_(1))`.

So, we get,

`(7-3)/(2-1)` = 4

`(12-7)/(3-2)` = 5

`(16-12)/(4-3)` = 4

`(19-16)/(5-4)` = 3

Since, the slope or the rate of change is not constant for different pairs of points.

Thus, the given function is not a linear function.