Question

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

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

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

• 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

$\Delta y_1=7-5=2$, $\Delta y_2=14-7=7$, $\Delta y_3=7-14=-7$, $\Delta y_4=5-7=-2$

Step3: Check linearity condition

For exact linearity, $\frac{\Delta y}{\Delta x}$ must be constant. $\frac{2}{1}
eq\frac{7}{1}
eq\frac{-7}{1}
eq\frac{-2}{1}$, so not exactly linear. The y differences do not follow a consistent approximate trend either.

Answer:

Nonlinear