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Question
Which table shows a proportional linear relationship between x and y?
Responses
A
x y
6 4
12 10
18 16
24 22
28 26x y 6 4 12 10 18 16 24 22 28 26
B
x y
7 15
8 17
14 29
16 33
17 35x y 7 15 8 17 14 29 16 33 17 35
C
x y
-9 54
-6 36
0 0
5 -30
7 -42x y -9 54 -6 36 0 0 5 -30 7 -42
D
x y
-15 -14
-13 -12
-11 -10
-9 -8
-7 -6
D
x y
-15 -14
-13 -12
-11 -10
-9 -8
-7 -6
To determine which table shows a proportional linear relationship between x and y, we need to check if the ratio between the values of x and y remains constant.
Let's calculate the ratios for each table:
Table A:
x1/y1 = 6/4 = 1.5
x2/y2 = 12/10 = 1.2
x3/y3 = 18/16 = 1.125
x4/y4 = 24/22 = 1.0909
x5/y5 = 28/26 = 1.0769
Table B:
x1/y1 = 7/15 = 0.4667
x2/y2 = 8/17 = 0.4706
x3/y3 = 14/29 = 0.4828
x4/y4 = 16/33 = 0.4848
x5/y5 = 17/35 = 0.4857
Table C:
x1/y1 = -9/54 = -0.1667
x2/y2 = -6/36 = -0.1667
x3/y3 = 0/0 = undefined (division by zero)
x4/y4 = 5/-30 = -0.1667
x5/y5 = 7/-42 = -0.1667
Table D:
x1/y1 = -15/-14 = 1.0714
x2/y2 = -13/-12 = 1.0833
x3/y3 = -11/-10 = 1.1
x4/y4 = -9/-8 = 1.125
x5/y5 = -7/-6 = 1.1667
From the calculations, we can see that Table A has a constant ratio between x and y, which means it shows a proportional linear relationship. So, the correct answer is A.
To determine which table shows a proportional linear relationship between x and y, we need to check if the ratio between the y-values and the corresponding x-values is constant.
For option A:
x: 6, 12, 18, 24, 28
y: 4, 10, 16, 22, 26
Let's find the ratios:
4/6 = 2/3
10/12 = 5/6
16/18 = 8/9
22/24 = 11/12
26/28 = 13/14
The ratios are not all equal, so option A does not show a proportional linear relationship.
For option B:
x: 7, 8, 14, 16, 17
y: 15, 17, 29, 33, 35
Let's find the ratios:
15/7 = 2.14
17/8 = 2.13
29/14 = 2.07
33/16 = 2.06
35/17 = 2.05
The ratios are not all equal, so option B does not show a proportional linear relationship.
For option C:
x: -9, -6, 0, 5, 7
y: 54, 36, 0, -30, -42
Let's find the ratios:
54/-9 = -6
36/-6 = -6
0/0 (undefined)
-30/5 = -6
-42/7 = -6
The ratios are all equal to -6, so option C shows a proportional linear relationship.
For option D:
x: -15, -13, -11, -9, -7
y: -14, -12, -10, -8, -6
Let's find the ratios:
-14/-15 = 14/15 ≈ 0.93
-12/-13 = 12/13 ≈ 0.92
-10/-11 = 10/11 ≈ 0.91
-8/-9 = 8/9 ≈ 0.89
-6/-7 = 6/7 ≈ 0.86
The ratios are not all equal, so option D does not show a proportional linear relationship.
Therefore, option C is the table that shows a proportional linear relationship between x and y.