This document discusses direct and inverse variations. It provides examples of how to set up and solve direct and inverse variation problems. Specifically, it explains: 1) Direct variation shows a relationship where as x increases, y increases or decreases at a constant rate. The formula is y1/x1 = y2/x2. 2) For a direct variation example where y=10 when x=2.4, it is solved by setting up as 10/2.4 = y/x and cross multiplying to find x=3.6 when y=15. 3) For an inverse variation, as one value goes up the other goes down, without a constant rate. The formula uses

1. Direct and
Inverse
Variations

2. 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.

3. Direct Variation
y1
x1

y2
x2
Direct variation uses the
following formula:

4. 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?

5. 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

6. Direct Variation
if y varies directly as x and y = 10
as x = 2.4, find x when y =15
10
2.4

15
x

7. Direct Variation
How do we solve this? Cross
multiply and set equal.
10
2.4

15
x

8. Direct Variation
We get: 10x = 36
Solve for x by diving both sides by 10.
We get x = 3.6

9. 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.

10. Direct Variation
If y varies directly with x and
y = 12 when x = 2, find y
when x = 8.
12
2

y
8

11. Direct Variation
Cross multiply: 96 = 2y
Solve for y. 48 = y.
12
2

y
8

12. 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.

13. Inverse Variation
With Direct variation we
Divide our x’s and y’s.
In Inverse variation we will
Multiply them.
x1y1 = x2y2

14. 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

15. 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