Question

Which relationship is a direct variation?

Answer 1

Option A is the relationship which shows a direct variation.

Step-by-step explanation:

The direct variation is a relationship between two variables in which one is the multiple of the other. It is given by the relation

$\frac{y}{x}=k$

Option A:

For $x=2$ and $y=1$,

$\frac{y}{x}=\frac{1}{2}$

For $x=4$ and $y=2$,

$\frac{y}{x}=\frac{2}{4}= \frac{1}{2}$

Since, the constant k is equal for all the values of x and y in the table, this relationship is a direct variation.

Option B:

For $x=2$ and $y=4$,

$\frac{y}{x}=\frac{4}{2}= 2$

For $x=4$ and $y=16$,

$\frac{y}{x}=\frac{16}{4} =4$

Since, the values of constant k is not equal for all the values of x and y in the table, this relationship is not a direct variation.

Option C:

For $x=1$ and $y=3$

$\frac{y}{x} =\frac{3}{1} =3$

For $x=2$ and $y=5$

$\frac{y}{x} =\frac{5}{2}$

Since, the values of constant k is not equal for all the values of x and y in the table, this relationship is not a direct variation.

Option D:

For $x=1$ and $y=-1$

$\frac{y}{x} =\frac{-1}{1} =-1$

For $x=2$ and $y=2$

$\frac{y}{x} =\frac{2}{2} =1$

Since, the values of constant k is not equal for all the values of x and y in the table, this relationship is not a direct variation.

Thus, Option A is the relationship which shows direct variation.