Which table represents a direct variation?
Table A
x
4
6
8
10
y
7
9
11
13
Table B
x
4
6
8
10
y
12
18
24
30
Table C
x
4
6
8
10
y
1
3
5
7
Table D
x
4
6
8
10
y
3
3
3
3
Table A
Table B
Table C
Table D
Table B
x
4
6
8
10
y
12 = 3*4
18 = 3*6
24 = 3*8
30 = 3*10
SO y = 3 x That looks pretty direct.
To determine which table represents a direct variation, we need to check if there is a constant ratio between the values of x and y. In direct variation, as one variable increases (or decreases), the other variable also increases (or decreases) by the same ratio. Let's analyze each table:
Table A:
The values of y increase by 1 each time x increases by 2. This means that the ratio between the values of x and y is constant: 4/7 = 6/9 = 8/11 = 10/13. Table A represents direct variation.
Table B:
The values of y increase by 6 each time x increases by 2. This means that the ratio between the values of x and y is not constant: 4/12 ≠ 6/18 ≠ 8/24 ≠ 10/30. Table B does not represent direct variation.
Table C:
The values of y increase by 2 each time x increases by 2. This means that the ratio between the values of x and y is not constant: 4/1 ≠ 6/3 ≠ 8/5 ≠ 10/7. Table C does not represent direct variation.
Table D:
The values of y remain constant, regardless of the value of x. This means that there is no ratio between the values of x and y. Table D does not represent direct variation.
So, the table that represents direct variation is Table A.