Question

the table shows a function. is the function linear or nonlinear?

x	y
\\( 2\frac{1}{5} \\)	8
\\( 8\frac{3}{5} \\)	0

linear
nonlinear

Explanation:

Step1: Convert mixed numbers to fractions

$3\frac{3}{5}=\frac{18}{5}$, $2\frac{1}{5}=\frac{11}{5}$, $8\frac{3}{5}=\frac{43}{5}$

Step2: Calculate first x difference

$\Delta x_1 = \frac{18}{5}-\frac{11}{5}=\frac{7}{5}$

Step3: Calculate first y difference

$\Delta y_1 = 10-8=2$

Step4: Calculate first rate of change

$\frac{\Delta y_1}{\Delta x_1}=\frac{2}{\frac{7}{5}}=\frac{10}{7}$

Step5: Calculate second x difference

$\Delta x_2 = \frac{43}{5}-\frac{18}{5}=\frac{25}{5}=5$

Step6: Calculate second y difference

$\Delta y_2 = 0-10=-10$

Step7: Calculate second rate of change

$\frac{\Delta y_2}{\Delta x_2}=\frac{-10}{5}=-2$

Step8: Compare the rates

$\frac{10}{7}
eq -2$, so the rate is not constant.

Answer:

nonlinear