www.VirtualNerd.com

How Do You Use the Formula for Direct Variation?

y varies directly with x. If y=35 when x=7, what is y when x=12?

Summary

  1. y and x are variables
  2. Our problem gives us that y=35 when x=7
  3. We want to know what y is when x=12
  4. y=kx is the formula for direct variation
  5. k is the constant of variation
  6. Plug our known values, y=35 and x=7, into the formula
  7. Divide by 7 on both sides
  8. k, the constant of variation, is 5
  9. Plug in k=5 and x=12 to find y
  10. 5•12=60, which is y

Notes

    1. y and x are variables
    2. When x=7, y=35
    1. y and x are variables
    2. What does y equal when x=12?
    1. 'Varies directly' means we can use the formula for direct variation
    1. The formula for direct variation is y=kx
    2. y and x are variables
    3. k is the constant of variation
    1. The formula for direct variation is y=kx
    2. y and x are variables
    3. k is the constant of variation
    1. y and x are variables
    2. k is the constant of variation
    1. Since y varies directly with x, we can use the formula for direct variation
    1. We want to know what y equals when x=12
    2. We need to know what the constant k is if we want to find y
    3. We can find k using the other information the problem gives us
    1. Our problem tells us that y=35 when x=7
    2. So we can use these values and our formula to find the constant k
    1. k is the constant of variation
    2. If we know k, we can figure out what y is when x=12
    1. So when we plug these values into the formula, we get 35=k•7
    2. We are given that y=35 when x=7
    1. Division is the opposite of multiplication
    2. So to undo the multiplication, we can divide both sides by 7 to get k by itself
    1. On the right the 7's cancel, leaving us with k
    2. On the left, 35/7=5
    3. So we have found that the constant of variation, k, is 5
    1. Since k is a constant, it doesn't change even if the values of y and x change
    2. So we can use it to solve our problem
    1. Now that we have a value for our constant k, we can solve for y
    1. The formula for direct variation is y=kx
    2. We found that k=5
    3. And we were given that x=12
    1. Plug k=5 and x=12 into the formula
    2. We get y=5•12
    1. Multiply 5•12 to get 60
    2. So y=60 when x=12