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

Explanation:

Step1: Calculate the slope between first two points

The formula for slope (m=\frac{y_2 - y_1}{x_2 - x_1}). For ((x_1,y_1)=(4,12)) and ((x_2,y_2)=(13,9)), (m_1=\frac{9 - 12}{13 - 4}=\frac{-3}{9}=-\frac{1}{3})

Step2: Calculate the slope between second and third points

For ((x_2,y_2)=(13,9)) and ((x_3,y_3)=(19,2)), (m_2=\frac{2 - 9}{19 - 13}=\frac{-7}{6})

Step3: Compare the slopes

Since (m_1 =-\frac{1}{3}\neq m_2=-\frac{7}{6}), the function is not linear.

Answer:

nonlinear