Question

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

x	-10	-1	17
y	19	10	-8

linear
nonlinear

Explanation:

Step1: Calculate x differences

$\Delta x_1 = -1 - (-10) = 9$, $\Delta x_2 = 17 - (-1) = 18$

Step2: Calculate y differences

$\Delta y_1 = 10 - 19 = -9$, $\Delta y_2 = -8 - 10 = -18$

Step3: Check constant slope

Slope 1: $\frac{\Delta y_1}{\Delta x_1} = \frac{-9}{9} = -1$
Slope 2: $\frac{\Delta y_2}{\Delta x_2} = \frac{-18}{18} = -1$

Answer:

linear