which table of values represents a linear function? a x y -3 -1 -1 1 1 3 3 5 b x y 1 7 3 5 5 4 7 2 c x y -3…

Explanation:

Step1: Recall slope - formula for linear functions

The slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For a linear function, the slope between any two points is constant.

Step2: Calculate slopes for Table A

For the first two points $(-3,-1)$ and $(-1,1)$: $m_1=\frac{1-(-1)}{-1 - (-3)}=\frac{2}{2}=1$. For the second and third points $(-1,1)$ and $(1,3)$: $m_2=\frac{3 - 1}{1-(-1)}=\frac{2}{2}=1$. For the third and fourth points $(1,3)$ and $(3,5)$: $m_3=\frac{5 - 3}{3 - 1}=\frac{2}{2}=1$. The slope is constant.

Step3: Calculate slopes for Table B

For the first two points $(1,7)$ and $(3,5)$: $m_1=\frac{5 - 7}{3 - 1}=\frac{-2}{2}=-1$. For the second and third points $(3,5)$ and $(5,4)$: $m_2=\frac{4 - 5}{5 - 3}=-\frac{1}{2}$. The slope is not constant.

Step4: Calculate slopes for Table C

For the first two points $(-3,8)$ and $(-2,5)$: $m_1=\frac{5 - 8}{-2-(-3)}=\frac{-3}{1}=-3$. For the second and third points $(-2,5)$ and $(2,-1)$: $m_2=\frac{-1 - 5}{2-(-2)}=\frac{-6}{4}=-\frac{3}{2}$. The slope is not constant.

Step5: Calculate slopes for Table D

For the first two points $(-1,9)$ and $(0,5)$: $m_1=\frac{5 - 9}{0-(-1)}=\frac{-4}{1}=-4$. For the second and third points $(0,5)$ and $(1,2)$: $m_2=\frac{2 - 5}{1 - 0}=-3$. The slope is not constant.

Answer:

A.

x	y
-3	-1
-1	1
1	3
3	5