# Direct and Inverse Variation - PowerPoint by fjwuxn

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```									  Direct and Inverse Variation

Take notes when you see
this animated pencil.

Take
Notes
Objectives

• Understand the specialized
vocabulary
• Know the basic algebraic equations
that represent direct and inverse
variation
• Apply techniques for classifying the
types of variation
Direct Proportion
Direct Variation
Directly Proportional
• A relationship between two variables in
which one is a “constant multiple” of the
other. When one variable changes the
“other changes in proportion” to the first.
• If y is directly proportional to x, the
equation is of the form y = kx (where k is a
constant).
Example of Direct Variation
• Equation: y = 3x         x        y     y/x
• Variable y is directly   0   3   0
proportional to x.
1        3    3/1=3
• Tripling x causes y to
triple.                  2   3   6    6/2=3
3        9    9/3=3
4        12   12/4=3
5        15   15/5=3
Graph of Direct Variation
y = 3x
y

x
Inverse Variation
Inverse Proportion
Inversely Proportional
• A relationship where the “product of two
variables is a constant”. When one
variable increases the other decreases in
proportion so that the “product is
unchanged”.
• If y is inversely proportional to x, the
equation is of the form y = k/x (where k is
a constant).
Example of Inverse Variation
• Equation: y = 48/x           x   y        xy
• Variable y is inversely      1   48       48
proportional to x.
3   2   24    1/3 48
• Tripling x causes y to
one third. The product       3   16       48
of x and y is always
48.                          4   12       48
6   8        48
8   6        48
Graph of Inverse Variation
y

20

18                                                     y = 48/x
16

14

12

10

8

6

4

2

0
0   2   4   6   8   10   12   14   16   18   20   x
Do the following Qs
1. If all the HKIS items in the Dragon Shop
are on sale for 85%, what will be the new
cost for the following:
a) a T-shirt that costs \$70 originally
b) a windbreaker jacket that cost \$130
originally
Do the following Qs
2. If the scale on a map reads
0.25 in. : 4 mi, calculate the following:
a) find the actual distance from
Metropolis to Smallville which has a
measured map distance of 9.25 in.
b) find the map distance from Smallville
to Roswell which has an actual
distance of 268 mi.
Do the following Qs
3. If model yachts are built to 1 in / 9 ft of
the actual size, calculate the following:
a) find the model length of a Blue Tooth
yacht which is 120 ft long.
b) find the actual length of a K2 yacht
which has a model length of 9.5 in.
Do the following Qs
4. Circle the correct terminology to make
true statements.
a) Knowing that the distance is equal to
speed times time (d = st), in a 100
meters sprint, any speed is directly
or inversely proportional to time?
b) If the speed is constant, then any
distance is directly or inversely
proportional to time?
Do the following Qs
5. Given that length and width are inversely
proportional to a constant area of 90 m2,
calculate the following:
a) If the length is 15 m, what is the
width?
b) If you want to create a box with an
area of 90 m2 that wraps around the
Earth’s equator, you require a width
of 38 million meters. What is the
length of the box?
Do the following Qs
6. Given that pressure (P) and volume (V)
are inversely proportional to each other
when temperature is constant, use
P1V1 = P2V2 to calculate the following.
a) If P1 = 1 atm and V1 = 4.5 Liters,
find P2, if V2 = 1.5 L?
b) If P1 = 0.5 atm and V1 = 4.5 Liters,
find V2, if P2 = 1.0 atm?
Do the following Qs
7. Circle the correct terminology to make
true statements.
In science, power (P) is defined by the
work (W) done in a certain amount of
time. P = W/t.
a) If the work done is constant, then
pressure is directly or inversely
proportional to time?
b) If the power is constant, then any
work done is directly or inversely
proportional to time?
Do the following Qs
8. In order to have objects balanced on a
double pan scale, the massleft times the
distanceleft must equal to massright times
the distanceright (mldl = mrdr).
50 g
20 g

15 cm           Distance ?

Calculate the distance needed away
from the fulcrum (pivot) so that the 50g
object will balance the left hand side.
Do the following Qs
9. In order to have objects balanced on a
double pan scale, the massleft times the
distanceleft must equal to massright times
the distanceright (mldl = mrdr).
5g
Mass ?
25 g

15 cm             20 cm

Calculate the mass needed to be placed
15 cm away from the fulcrum (pivot) so
that it will balance the right hand side.
Do the following Qs
10. In order to have objects balanced on a
double pan scale, the massleft times the
distanceleft must equal to massright times
the distanceright (mldl = mrdr).
50 g
20 g    20 g

5 cm          5 cm

Distance ?

Calculate the distance needed away
from the fulcrum (pivot) so that the
scale is balance.

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