direct or inverse variations

When x = 2, y = 12. Find the value of y when x = 4 if
y varies directly as x²

Answer explanation

y = kx²
With the given (2,12) we find k
12 = k(2²)

k = 12/4

k = 3

so y = 3x²

Then y = 3(4²)

y = 3(16)
y = 48.

When x = 2, y = 12. Find the value of y when x = 4 if
y varies inversely as x.

Answer explanation

y = k/x
We use the given (2,12) to find k
k = xy
k = 2(12)
k = 24.
So y = 24/x
then y = 24/4
y = 6.

y = 24 when x = 5. Find the value of x when y = 2 if
y varies directly as x.

• 24/5

• 48/5

• 5/12

• 10/12

Answer explanation

y =kx
We use the given (5,24) to find k.
k = y/x
k = 24/5 ---- keep the fraction for accuracy purpose
y = (24/5)x
Find x when y =2.
x = 5y/24
x = 5(2)/24
x = 5/12

y = 24 when x = 5. Find the value of x when y = 2 if
y varies inversely as x³.

• 3000

• 1500

x=1, y=1
x=2, y = 8
x=3, y =27
x=4, y =64
The values are part of a function where

• y varies directly as x

• y varies directly as x³

• y varies inversely as x

• y varies inversely as x³

Answer explanation

Notice that
1³=1
2³=8
3³=27
4³=64
so y varies directly as x³.

x=-2, y=20
x=0, y = 0
x=3, y =45
x=4, y =80
Find the proportional constant k in y = kx².

• 5

• -5

• 1/5

• -1/5

Answer explanation

k = y/x²
Let us check with (-2,20)
k = 20/4
k = 5
check with (3,45)
k = 45/9
k = 5
check with (4,80)
k = 80/16
k = 5

x=-2, y=20
x=0, y = 0
x=3, y =45
x=4, y =80
These values are from a function where

• y varies directly with x

• y varies directly with x²

• y varies inversely with x²

• y varies inversely with x³

Answer explanation

k = y/x²
Let us check with (-2,20)
k = 20/4
k = 5
check with (3,45)
k = 45/9
k = 5
check with (4,80)
k = 80/16
k = 5

So y = 5x² so y varies direcly with x²

x =-2, y =-0.5
x =0, y is undefined
x=2, y =0.5
x=5, y=0.035
Values above come from a function when y varies inversely as x.

• True

• False

Answer explanation

False. If y = k/x
then with (-2, -1/2) then we have y = 1/x
but y =1/x does not fit the last data (5, 0.035)

x=2, y=30
x=4, y =15
x=6, y =10
x=12, y =5
These values are from a function where y varies ____ as x.

Answer explanation

Notice that xy is always 60.
So the proportionality constant k = 60
k = xy then y = k/x.
Thus, y is varies inversely as x.

x=2, y=30
x=4, y =15
x=6, y =10
x=12, y =5
Find the proportionality constant of the function for these values.

Answer explanation

Notice that xy is always 60.
So the proportionality constant k = 60
k = xy then y = k/x.
In this case, y is varies inversely as x.