Question

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

x	y
2	8
3	16
4	8
5	5

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

• exactly linear
• approximately linear
• nonlinear

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

$\Delta y_1=8-5=3$, $\Delta y_2=16-8=8$, $\Delta y_3=8-16=-8$, $\Delta y_4=5-8=-3$

Step3: Check linearity (constant slope)

Slope1: $\frac{\Delta y_1}{\Delta x_1}=3$, Slope2: $\frac{\Delta y_2}{\Delta x_2}=8$, Slope3: $\frac{\Delta y_3}{\Delta x_3}=-8$, Slope4: $\frac{\Delta y_4}{\Delta x_4}=-3$
Slopes are not constant, so data is not linear.

Answer:

Nonlinear