Question

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=\frac{13}{5}, y=5$$

Short answer

The inverse variation equation that represents the relationship between x and y is \(xy = 13\).

Step-by-step solution

Understanding Inverse Variation

If two variables x and y vary inversely, this means that their product is a constant. This can be written in mathematical form as \(xy = k\), where k is the constant of variation.

Calculating the Constant of Variation

Substitute the given x and y values into the formula. Therefore, when \(x= \frac{13}{5}\) and \(y=5\), we can calculate \(k = x * y = \frac{13}{5} * 5 = \frac{65}{5} = 13\). Here, 13 is the constant of variation.

Writing the Inverse Variation Equation

Now we can put the constant k into the original formula \(xy = k\), we have the inverse variation equation \(xy = 13\). This equation represents the inverse relationship between x and y.