Question

Use the table below to determine whether or not the cost to hire a web designer is a linear function of the number of hours worked?

Answer 1

Answer: B) Non Linear

In order to find out whether a table is linear or not, the numbers have to have a constant rate of change. in order to see whether they do have a constant rate of change or not, try to count the difference between each number on one side, then the other, and see if the difference is the same.

For instance, the total cost numbers go from $205 to $400, which is a $195 difference. Then it goes from $400 to $595, which is again a $195 difference, but pay attention to how it goes from $595 to $725, which is a $130 difference. That $130 difference automatically makes the graph non linear, since the rate of change for the total cost isn’t a constant $195. Just to be sure, you can check the other side as well.

The Hours go from 2 to 5 (3 hour difference), then 5 to 8 (another 3 hour difference), but then 8 to 10. Since the rate of change isn’t 3 hours through the entire Hour side, the table doesn’t have a constant rate of change, which makes this table a non linear function.

If a table doesn’t have a constant rate of change, it’s non-linear. If a table does have a constant rate of change, it is linear. In this case, since the table doesn’t have a constant rate of change, it’s not linear. This responses is kinda long, but I hope it helped!