For class 8th

2. 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 corressponding increase or decrease
in another quantity such that the ratio
remains constant is direct variation.

3. Direct Variation uses the following formula:

4. 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. 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. If y varies directly as x and y = 10
as x = 2.4,
find x when y = 15

7. How do we solve this ? Cross multiply and
set equal.

8. We get: 10x = 36
Solve for x by dividing both sides
by 10
We get x = 3.6

9. 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 and time to do a
particular journey.

10. With Direct variation we
divide our x’s and y’s.
In Inverse variation we will
multiply them.
x1y1 = x2y2

11. 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

12. 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