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? \

$$\begin{tabular}{|c|c|c|c|c|c|} \\hline x & 1 & 2 & 3 & 4 & 5 \\\\ \\hline y & 3 & 5 & 9 & 11 & 15 \\\\ \\hline \\end{tabular}$$

\bigcirc approximately linear \bigcirc nonlinear \bigcirc exactly 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

$\Delta y_1=5-3=2$, $\Delta y_2=9-5=4$, $\Delta y_3=11-9=2$, $\Delta y_4=15-11=4$

Step3: Check linearity condition

For exact linearity, $\frac{\Delta y}{\Delta x}$ must be constant. Here $\frac{2}{1}
eq\frac{4}{1}$, so not exactly linear. The y differences alternate between 2 and 4, not close enough to be approximately linear.

Answer:

Nonlinear