www.VirtualNerd.com

How Do You Write an Equation for Direct Variation from a Table?

Leo has started selling tutorials to educational companies. The following table relates the total profit (y) for tutorials made (x). Write a direct variation equation to describe this relation.

Summary

  1. The table relates the profit to the number of tutorials made
  2. A relation is a set of ordered pairs
  3. We put (2,4), (4,8), and (16,32) inside curly braces to show that they are a set
  4. y=kx is the equation for direct variation, where k is our constant of variation
  5. We're going to plug in (16,32) to find the constant of variation
  6. The constant of variation for this relation is 2

Notes

    1. The number of tutorials made is x, and the profit is y
    2. x and y are variables
    1. x is the variable representing the number of tutorials Leo made
    2. y is the variable representing the amount of profit Leo made
    3. In this case, Leo made 2 tutorials and gained a profit of 4
    1. x is the variable representing the number of tutorials Leo made
    2. y is the variable representing the amount of profit Leo made
    3. In this case, Leo made 4 tutorials and gained a profit of 8
    1. x is the variable representing the number of tutorials Leo made
    2. y is the variable representing the amount of profit Leo made
    3. In this case, Leo made 16 tutorials and gained a profit of 32
    1. The relation from the table is the set of ordered pairs including (2,4), (4,8), and (16,32)
    1. We're going to use the relation we just found to find the direct variation equation
    1. k is the constant of variation in the direct variation equation y=kx
    1. k is the constant of variation in the direct variation equation y=kx
    2. If we plug one of our ordered pairs into the equation, we'll be able to solve for k
    1. Our relation is the set of ordered pairs (2,4), (4,8), and (16,32)
    2. The x's are 2, 4, and 16
    3. The y's are 4, 8, and 32
    1. y=kx is the equation for direct variation
    1. Our relation is the set of ordered pairs (2,4), (4,8), and (16,32)
    2. We're going to take one of the ordered pairs from our relation and plug it into the equation y=kx
    1. Our relation is the set of ordered pairs (2,4), (4,8), and (16,32)
    2. We're going to take one of the ordered pairs from our relation and plug it into the equation y=kx
    3. k is the constant of variation
    1. We're plugging the ordered pair (16,32) into our direct variation equation y=kx
    1. We're plugging the ordered pair (16,32) into our direct variation equation y=kx
    1. Solving 32=k•16 for k gives us k=32/16=2
    1. Now that we have our constant of variation, we can plug it into the formula to get our direct variation equation for this relation
    1. The general form of a direct variation equation is y=kx, and we found k to be equal to 2