Question

Which of the following is true?

• A. Y is directly proportional to X then, Y = k X, where k is a constant
• B. Y is directly proportional to X then, Y = k X, where k is a variable
• C. Y is indirectly proportional to X then, Y = k X, where k is a constant
• D. Y is indirectly proportional to X then, Y = k X, where k is a variable

Answer 1

The correct option is A Y is directly proportional to X then, Y = k X, where k is a constant

If the two quantities are directly proportional, the increase of one quantity will increase the other quantity and vice versa.

For example:
$\text{Cost of 1 biscuit pack}=\$2\text{Here,}\frac{\text{cost}}{\text{quantity}}=\frac{2}{1}=2\text{Cost of 2 biscuit pack}=\$4\text{Here,}\frac{\text{cost}}{\text{quantity}}=\frac{4}{2}=2$

Here we can see that if the quantity of the biscuit increases, the cost is also increased, hence this relation is said to be direct proportions

$\frac{\text{cost}}{\text{quantity}}=\text{Constant (k)}$

Similarly when Y and X are in direct proportion
$\frac{Y}{X}=k$
or
$Y=kX$ where, k is constant
Hence, Option A is corrrect.