Direct and
Inverse
Variations
Direct Variation
When we talk about a direct
variation, we are talking about
a relationship where as
x increases,
y increases
or decreases at a CONSTANT
RATE.
Direct Variation
Direct variation uses the
following formula:
y1 y 2

x1 x 2
Direct Variation
example:
if y varies directly as x
and y = 10 as x = 2.4,
find x when y =15.
what x and y go together?
Direct Variation
If y varies directly as x and y = 10
find x when y =15.
y = 10, x = 2.4
make these y1 and x1
y = 15, and x = ?
make these y2 and x2
Direct Variation
if y varies directly as x and y = 10
as x = 2.4, find x when y =15
10 15

2.4
x
Direct Variation
How do we solve this? Cross
multiply and set equal.
10 15

2.4
x
Direct Variation
We get: 10x = 36
Solve for x by diving both sides by 10.
We get x = 3.6
Direct Variation
Let’s do another.
If y varies directly with x
and y = 12 when x = 2,
find y when x = 8.
Set up your equation.
Direct Variation
If y varies directly with x and
y = 12 when x = 2, find y
when x = 8.
12 y

2 8
Direct Variation
12 y

2 8
Cross multiply: 96 = 2y
Solve for y.
48 = y.
Inverse Variation
Inverse is very similar to
direct, but in an inverse
relationship as one value goes
up, the other goes down.
There is not necessarily a
constant rate.
Inverse Variation
With Direct variation we
Divide our x’s and y’s.
In Inverse variation we will
Multiply them.
x1y1 = x2y2
Inverse Variation
If y varies inversely with x and
y = 12 when x = 2, find y when x = 8.
x1y1 = x2y2
2(12) = 8y
24 = 8y
y=3
Inverse Variation
If y varies inversely as x and x = 18
when y = 6, find y when x = 8.
18(6) = 8y
108 = 8y
y = 13.5