This document discusses direct and inverse variations. It provides examples of how to set up and solve direct and inverse variation problems. For direct variation, as one variable increases, the other increases at a constant rate. The formula is y=kx, where k is the constant rate of change. For inverse variation, as one variable increases, the other decreases. To solve inverse problems, the formula used is x1y1=x2y2, where x1 and y1 are the known values and x2 is the unknown value being solved for. Examples of setting up and solving both direct and inverse variation word problems are provided.

1. Direct and Inverse
Variations
Name:- Manpreet Singh
Class:- VIII-J

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

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

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
12
2
y
8
Cross multiply: 96 = 2y
 Solve for y.
48 = y.


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

16. Thank You for Watching
This