Answer:
We conclude that 'Table B' represents a direct variation.
Step-by-step explanation:
We know that when y varies directly with x, the equation is
y ∝ x
y = kx
k = y/x
where 'k' is called the constant of proportionality.
Table A
x 4 6 8 10
y 7 9 11 13
Finding k for all the pairs of x and y
k = y/x
k = 7/4, k = 9/6 = 3/2, k = 11 / 8, k = 13/11
As constant of proportionality 'k' does not remain constant.
Hence, table A does not represent a direct variation
Table B
x 4 6 8 10
y 12 18 24 30
Finding k all the pairs of x and y
k = y/x
k = 12/4 = 3, k = 18/6 = 3, k = 24/8 = 3, k = 30/10 = 3
As the constant of proportionality remains constant.
Therefore, the value of k = 3 for all the points in the table.
Hence, table B represents a direct variation.
Table C
x 4 6 8 10
y 1 3 5 7
Finding k all the pairs of x and y
k = y/x
k = 1/4, k = 3/6 = 1/2, k = 5/8, k = 7/10
As the constant of proportionality 'k' does not remain constant.
Hence, table C does not represent a direct variation.
Table D
x 4 6 8 10
y 3 3 3 3
Finding k all the pairs of x and y
k = y/x
k = 3/4, k = 3/6, k = 3/8, k = 3/10
As the constant of proportionality 'k' does not remain constant.
Hence, table D does not a direct variation.
Therefore, we conclude that 'Table B' represents a direct variation.
