Lean direct and Inverse variatons

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
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