Question

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=2, y=5$$

Short answer

The equation that relates x and y is \(y = 10/x\)

Step-by-step solution

Understand the relationship between the variables

The variables x and y vary inversely. Hence, the equation relating them is \(xy = k\), where 'k' is the constant value that the product of x and y always equals.

Substitute the given values of x and y in the equation

Substitute the given values x=2 and y=5 in the equation \(xy=k\). Hence, we get \(2*5=k\) or \(k=10\).

Write the equation that relates x and y

Now that we have the value of 'k', we can write the equation that relates x and y. Hence, the equation is \(xy=10\) or re-arranging for y we get \(y=10/x\).