Question

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

x	1	2	3	4	5
y	5	8	14	17	23

options: nonlinear, exactly linear, approximately linear

Explanation:

Step1: Calculate x differences

$\Delta x_1=2-1=1$, $\Delta x_2=3-2=1$, $\Delta x_3=4-3=1$, $\Delta x_4=5-4=1$

Step2: Calculate y differences

$\Delta y_1=8-5=3$, $\Delta y_2=14-8=6$, $\Delta y_3=17-14=3$, $\Delta y_4=23-17=6$

Step3: Check linearity consistency

Linear data needs constant $\frac{\Delta y}{\Delta x}$. Here $\frac{3}{1}=3$, $\frac{6}{1}=6$ (not constant).

Answer:

Nonlinear