# If y is inversely proportional to x, and y = 8 when x = 2, find y when x = 5.

## Question:

If y is inversely proportional to x, and y = 8 when x = 2, find y when x = 5.

## Inverse Variation:

Inverse variation or inverse proportional propotional explains the relationship between two variables which change in the opposite direction. The product of such variables gives us a constant which is known as the proportionality constant.

Given that {eq}y {/eq} varies inversely proportional to {eq}x {/eq}, we can write this relation as:

• {eq}y\propto \dfrac{1}{x} {/eq}

Removing the proportionality constant, we get an equation:

• {eq}y = \dfrac{k}{x} {/eq}, where k is the constant of variation.

Given that {eq}y = 8 {/eq} when {eq}x = 2 {/eq}, the constant of variation is equal to:

• {eq}8 = \dfrac{k}{2} {/eq}
• {eq}k = 8\times 2 = 16 {/eq}

Thus, an equation that explains the relationship between x and y is equal to:

• {eq}y = \dfrac{16}{x} {/eq}

Using the above equation, the value of y when x = 5 is equal to:

• {eq}y = \dfrac{16}{5} = \boxed{3.2} {/eq}