This document discusses direct and inverse variations. Direct variation means that as one variable increases, the other increases or decreases at a constant rate. The relationship can be expressed as y1/x1 = y2/x2. Inverse variation means that as one variable increases, the other decreases. The relationship is expressed as x1y1 = x2y2. Examples are provided of setting up and solving direct and inverse variation problems to find unknown variables.

2. Direct and
Inverse
Variations

3.  Variation in general , will concern two
variables; say height and weight of a
person, and how , when one of these
changes, the other might be expected
to change.

4. 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.

5. Direct variation
 We have Direct Variation, if the two
variables change in the same sense, that
is, if one increases, so does the other.
 An increase or decrease in one quantity
with a corresponding increase or
decrease in another quantity such that
the ratio remains constant is called
direct variation.

6. Direct Variation
y1
x1
=
y2
x2
Direct variation uses the
following formula:

7. 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?

8. 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

9. 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

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

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

12. 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.

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

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

15. 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.

16. Inverse Variation
 When two quantities vary inversely, an
increase in one leads to the decrease in
the other quantity and vice-versa, in
inverse ratio.
 We have inverse variation if one going
up causes the other to go down. An
example of this might be speed & time
to do a particular journey.

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

18. 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

19. 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