in which table is y a non - linear function of x?\na.\n| x | y |\n| -2 | 2.0 |\n| 3 | 4.5 |\n| 4 | 5.0…

Explanation:

Step1: Recall linear function property

A linear function has a constant rate of change (slope), calculated as (m = \frac{y_2 - y_1}{x_2 - x_1}) for any two points ((x_1,y_1)) and ((x_2,y_2)). We'll check the slope between consecutive (or any) points in each table.

Step2: Check Table A

Points: ((-2, 2.0)), ((3, 4.5)), ((4, 5.0)) Slope between ((-2,2.0)) and ((3,4.5)): (m_1=\frac{4.5 - 2.0}{3 - (-2)}=\frac{2.5}{5}=0.5) Slope between ((3,4.5)) and ((4,5.0)): (m_2=\frac{5.0 - 4.5}{4 - 3}=\frac{0.5}{1}=0.5) Constant slope, so linear.

Step3: Check Table B

Points: ((-1, 2)), ((0, -1)), ((4, -13)) Slope between ((-1,2)) and ((0,-1)): (m_1=\frac{-1 - 2}{0 - (-1)}=\frac{-3}{1}=-3) Slope between ((0,-1)) and ((4,-13)): (m_2=\frac{-13 - (-1)}{4 - 0}=\frac{-12}{4}=-3) Constant slope, so linear.

Step4: Check Table C

Points: ((-3, -5.5)), ((-1, -2.5)), ((5, 6.5)) Slope between ((-3,-5.5)) and ((-1,-2.5)): (m_1=\frac{-2.5 - (-5.5)}{-1 - (-3)}=\frac{3}{2}=1.5) Slope between ((-1,-2.5)) and ((5,6.5)): (m_2=\frac{6.5 - (-2.5)}{5 - (-1)}=\frac{9}{6}=1.5) Constant slope, so linear.

Step5: Check Table D

Points: ((-4, 12)), ((-2, 8)), ((1, 4)) Slope between ((-4,12)) and ((-2,8)): (m_1=\frac{8 - 12}{-2 - (-4)}=\frac{-4}{2}=-2) Slope between ((-2,8)) and ((1,4)): (m_2=\frac{4 - 8}{1 - (-2)}=\frac{-4}{3}\approx -1.33) Slopes are not equal, so non - linear.

Answer:

D. The table with (x) values (-4, -2, 1) and (y) values (12, 8, 4) (i.e., Table D)