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How Do You Use the Formula for Inverse Variation to Write an Equation?

If y varies inversely as x and y = 8 when x = 6, find y when x = 12.

Summary

  1. x and y are variables
  2. xy=k is the formula for inverse variation
  3. k is the constant of inverse variation
  4. Use the values the problem gives, x=6 and y=8, to find k
  5. 6•8=48, which is k
  6. Plug in 12 for x and 48 for k to find y
  7. Divide both sides by 12 to solve for y
  8. 48/12=4, which is y

Notes

    1. y and x are variables
    2. When x=6, y=8
    1. y and x are variables
    2. When x=12, what is y?
    1. 'Varies inversely' means we're talking about inverse variation
    2. So we can use the formula for inverse variation to find y
    1. We can use the formula for inverse variation to find y
    2. The formula for inverse variation is xy=k, where k is a constant and x and y are variables
    1. The formula for inverse variation is xy=k, where k is a constant and x and y are variables
    1. x and y are variables
    2. k is the constant of inverse variation
    3. k stays the same even if x and y change
    1. Our problem says that y varies inversely as x
    2. So we can use the formula for inverse variation to solve for y
    1. Our problem gives us a value for x, 12
    2. y is our unknown variable
    1. We can use the other information in our problem to find k
    2. Since k is a constant, it won't change even if x and y change
    1. Since k is a constant, it won't change even if x and y change
    2. So we can plug the other values our problem gives us, y=8 and x=6, into the formula to find k
    1. Since k is a constant, it won't change even if x and y change
    2. So we can plug the other values our problem gives us, y=8 and x=6, into the formula to find k
    1. We were given that y=8 when x=6
    1. Plugging these values into the formula xy=k gives us 6•8=k
    1. 6•8=48
    2. So our constant k=48
    1. We can use this value for k to solve our original problem
    1. Now we have a value for k, 48, and for x, 12
    2. We can plug these into the formula xy=k to find y
    1. y is our unknown variable
    1. Our formula is xy=k
    2. We know that x=12 and k=48
    3. So our formula becomes 12y=48
    1. Division is the opposite of multiplication
    2. So dividing by 12 on both sides will undo the multiplication so we can get y by itself
    1. On the left the 12's cancel, leaving us with y
    2. On the right, 48/12 is 4