Question

In which of the following relation, $x$ and $y$ are not in proportion?

• A. $xy=12$
• B. $\frac{x}{y}=3$
• C. $y=x+6$
• D. $\frac{x}{y}=\frac{1}{2}$

Answer 1

The correct option is C $y=x+6$

$\left(i\right)$ $xy=12$
As the value of $xy$ is a constant $x$ is inversely proportional to $y$.

$\left(ii\right)$$\frac{x}{y}=3$
As the value of $\frac{x}{y}$ is a constant $x$ is directly proportional to $y$.

$\left(iii\right)$$y=x+6$

$xy=x(x+6)=x^2+6x$ which is not a constant

And $\frac{y_1}{y_2}=\frac{x_1+6}{x_2+6}$

That means $\frac{y_1}{y_2}\ne \frac{x_1}{x_2}$

From the above conditions, we can say that $y$ is not in proportion with $x$.

$\left(iv\right)$$\frac{x}{y}=\frac{1}{2}$
As the value of $\frac{x}{y}$ is a constant $x$ is directly proportional to $y$.