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

Answer:

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

Step-by-step 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, $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

So, we get,

$\frac{7-3}{2-1}$ = 4

$\frac{12-7}{3-2}$ = 5

$\frac{16-12}{4-3}$ = 4

$\frac{19-16}{5-4}$ = 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.