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.
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
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