Question

The relation between $x$ and $y$ is $y=2x+3$.

Here $y$ varies _______.

• A. Directly with $x$
• B. inversely with $x$
• C. Not in proportion with $x$
• D. (a) and (b) above.

Answer 1

The correct option is C Not in proportion with $x$

Two variables are said to be in inverse proportion if the product of the two variables is constant.

Given, $y=2x+3$,

$\Rightarrow xy=x(2x+3)=2x^2+3x$, which is not a constant.
So, '$x$' and '$y$' are not in inverse proportion.

Two variables are said to be in direct proportion if their ratio is constant.

And $\frac{y}{x}=2+\frac{3}{x}$, which is not a constant.

$\therefore$ '$x$' and '$y$' are not in direct proportion.

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