For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7?

Solution:

When we usually talk about relationships between two variables, primarily there can be two types of relationships. The first one is a direct relationship and another an inverse relationship.

In a direct variation, as x increases y increases, or as x decreases, y decreases. Mathematically or symbolically we can write the relationship as:

x ∝ y

x = ky where k is the constant of proportionality

In an indirect variation as x increases y decreases, or as x decreases y increases. Mathematically or symbolically we can write the relationship as:

x ∝ 1/y

x = k/y where k is the constant of proportionality.

Or

k=xy

The given equation xy = k is an inverse variation equation which implies that x, and y vary inversely with each other and their product is a constant k.

Now given that y = 4 and k = 7, the value of x can be calculated as below:

x(4) = 7

x = 7/4

For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7?

Summary:

The value of x which satisfies the relation xy = k when x = 4 and k = 7 is x = 7/4.