Question

without graphing, determine if the following data set is exactly linear, approximately linear, or nonlinear.

x	y
1	5
2	7
3	14
4	7
5	5

is the data set exactly linear, approximately linear, or nonlinear?
approximately linear
exactly linear
nonlinear

Explanation:

Step1: Calculate first - differences of y - values

For \(x = 1\) to \(x = 2\), \(\Delta y_1=7 - 5=2\); for \(x = 2\) to \(x = 3\), \(\Delta y_2=14 - 7 = 7\); for \(x = 3\) to \(x = 4\), \(\Delta y_3=7 - 14=-7\); for \(x = 4\) to \(x = 5\), \(\Delta y_4=5 - 7=-2\).

Step2: Analyze the first - differences

In a linear function, the first - differences of \(y\) values for equally - spaced \(x\) values are constant. Here, the first - differences \(2,7, - 7,-2\) are not constant.

Answer:

Nonlinear