Enter the x, y, and z values into the calculator to determine the joint variation constant. Then, enter two new values to solve the missing value of a joint variation problem.

## Joint Variation Formula

The following formula is used in join variation problems.

y = k*x*z
• Where k is the joint variation constant
• x, y, and z are points or variables that depend on the constant k

To calculate a joint variation, multiply the joint variation constant by the variables.

## Joint Variation Definition

What is join variation? A joint variation is a problem in which a single variable is dependent, and varies jointly, with two more other variables. In the case of the equation above, the variable y varies with both x and z.

## Join Variation Example Problem

How to solve a joint variation problem?

1. First, determine the variation constant.

In this example, we have a variable y that varies with changes in variables x and z. One set of data points shows that when y = 10, x=1 and z=5. To solve for k, we re-arrange the equation, k = y/ x*z = 10 / (1*5) = 2.

2. Next, determine additional data points.

For this problem, we also know that x = 3 and z = 8 at another point.

3. Finally, calculate y at the new points.

Using the formula above, and our constant from step 1, we can find the y coordinate or variable value. y = 2*3*8 = 48.

## About Join Variation

Can joint variation be considered direct variation? A join variation is a case in which two or more variables are directly related. A direct variation is defined as one variable that is a constant multiple of another variable. So, while they are similar, they are not exactly the same.