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 join variation constant
  • x, y, and z are points or variables that depend on the constant k

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.

joint variation calculator
joint variation formula