1. If y varies directly as x and x = 4 when y = 2. find k

Solution:
`y prop x`

`=>y=k*x`

Now, `x=4" when "y=2`

`=>2=k*4`

`=>k=(2)/(4)`

`=>k=1/2`

Hence, `y=1/2*x`

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2. y prop x and x=4 when y=20. find constant

Solution:
`y prop x`

`=>y=k*x`

Now, `x=4" when "y=20`

`=>20=k*4`

`=>k=(20)/(4)`

`=>k=5`

Hence, `y=5*x`

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3. If y varies directly as x and x = 12 when y = 9. find equation

Solution:
`y prop x`

`=>y=k*x`

Now, `x=12" when "y=9`

`=>9=k*12`

`=>k=(9)/(12)`

`=>k=3/4`

Hence, `y=3/4*x`

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4. If y varies directly as x^2 and x = 2 when y = 8. find constant

Solution:
`y prop x^2`

`=>y=k*x^2`

Now, `x=2" when "y=8`

`=>8=k*2^2`

`=>8=k*4`

`=>k=(8)/(4)`

`=>k=2`

Hence, `y=2*x^2`

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5. If y varies directly as square root of x and x = 4 when y = 8. find k

Solution:
`y prop sqrt(x)`

`=>y=k*sqrt(x)`

Now, `x=4" when "y=8`

`=>8=k*sqrt(4)`

`=>8=k*2`

`=>k=(8)/(2)`

`=>k=4`

Hence, `y=4*sqrt(x)`

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