Question

1. which table represents a non - proportional relationship between x and y?

a

x	y
1	-4
3	-12
7	-28
15	-60

c

x	y
-17	93.5
-5	27.5
2	-11
10	-55

b

x	y
1	7.5
4	30
7	52.5
10	75

d

x	y
-5	11
-1	-1
1	-7
8	-28

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship between \(x\) and \(y\) means \(y = kx\) (where \(k\) is a constant), so \(\frac{y}{x}\) should be constant for all pairs \((x,y)\) ( \(x
eq0\) ). We check each table.

Step2: Check Table A

For \(x = 1,y=-4\): \(\frac{y}{x}=\frac{-4}{1}=-4\)
For \(x = 3,y=-12\): \(\frac{-12}{3}=-4\)
For \(x = 7,y=-28\): \(\frac{-28}{7}=-4\)
For \(x = 15,y=-60\): \(\frac{-60}{15}=-4\)
All ratios are \(-4\), so proportional.

Step3: Check Table B

For \(x = 1,y=7.5\): \(\frac{7.5}{1}=7.5\)
For \(x = 4,y=30\): \(\frac{30}{4}=7.5\)
For \(x = 7,y=52.5\): \(\frac{52.5}{7}=7.5\)
For \(x = 10,y=75\): \(\frac{75}{10}=7.5\)
All ratios are \(7.5\), so proportional.

Step4: Check Table C

For \(x=-17,y = 93.5\): \(\frac{93.5}{-17}=-5.5\)
For \(x=-5,y = 27.5\): \(\frac{27.5}{-5}=-5.5\)
For \(x = 2,y=-11\): \(\frac{-11}{2}=-5.5\)
For \(x = 10,y=-55\): \(\frac{-55}{10}=-5.5\)
All ratios are \(-5.5\), so proportional.

Step5: Check Table D

For \(x=-5,y = 11\): \(\frac{11}{-5}=-2.2\)
For \(x=-1,y=-1\): \(\frac{-1}{-1}=1\)
The ratios \(-2.2\) and \(1\) are not equal, so non - proportional.

Answer:

D. The table with \(x\) values \(-5, - 1,1,8\) and corresponding \(y\) values \(11,-1,-7,-28\) (the table labeled D)