Question

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

x	-10	-3 2/3	2 2/3
y	2	-2 3/4	-7 1/2

linear
nonlinear

Explanation:

Step1: Calculate Δx (x differences)

$\Delta x_1 = -3 - (-10) = 7$, $\Delta x_2 = 2 - (-3) = 5$

Step2: Calculate Δy (y differences)

$\Delta y_1 = -2\frac{3}{4} - 2 = -\frac{15}{4}$, $\Delta y_2 = -7\frac{1}{2} - (-2\frac{3}{4}) = -\frac{19}{4}$

Step3: Check constant rate of change

For linearity, $\frac{\Delta y}{\Delta x}$ must be constant.
$\frac{\Delta y_1}{\Delta x_1} = \frac{-\frac{15}{4}}{7} = -\frac{15}{28}$, $\frac{\Delta y_2}{\Delta x_2} = \frac{-\frac{19}{4}}{5} = -\frac{19}{20}$
These values are not equal, so the rate of change is not constant.

Answer:

nonlinear