Question

How do you determine if the following data set is linear or quadratic: (-4,10), (-3,7), (-2,4), (-1,1), (0,-2)?

Answer 1

Firstly, you should try to plot this data set in order to see the behavior of it.

We can start with converting it to table to see the effect of the variable `x` on dependent variable `y`.

As you can see from the table, a one unit increase in `x` results in 3 units decrease in `y`. Therefore, the dependent variable `y` changes at a constant rate with the independent variable `x`. Since the data set exhibits a constant rate of change, it is therefore plausible to graphically represent it by a line that is depicted below.

Plotting the data set is quite important to understand the behavior of the function and we can easily see that we are dealing with a data set which is linear for this case. If it was quadratic, we wouldn't be able to graphically represent it by a single line.

Linear and Non Linear Functions