5. Inverse variation occurs whenever
situations produce pairs of numbers
whose product is constant. For two
quantities x and y, an increase in x
causes a decrease in y or vice versa.
6. We can say that y varies inversely as
x or =
𝑘
𝑥
. The statement, “y varies
inversely as x,” translate to 𝑦 =
𝑘
𝑥
where k is the constant of variation.
7. Illustrative Example 1: The table below shows
the relationship that exist between the length (l)
and the width (w) of a rectangle whose area (A)
is 36 sq. units
8. The graph of the relation of the two
quantities, length (l) and width (w).
9. a. How do the length and the width
affect each other?
*As the length of the rectangle
increases, the width decreases.
11. c. Is there a constant number involved?
Explain the process that you have used in
finding out.
*Yes. Multiplying the values of the
length and width gives us the
constant.
12. d. How will you describe the
graph?
* The graph is not a straight line
13. Juan Paulo is riding on his bicycle in going
to school. He is traveling at 8 mph and
cover 8 miles in 1 hour. If his speed
decreases to 4 mph, it will take him 2 hours
to cover the same distance. Some possible
speeds and length of time to take him to
school are as follows.
16. The statement “y varies inverse
as x” is =
𝑘
𝑥
. Express each of
the following as equation.
17. a. The number of slices (s) that
can be made from a standard
Pinoy loaf of bread is inversely
proportional to the thickness (t)
of a slice.
Challenge
18.
19. b. At a constant voltage, the
electric current (I) varies
inversely as the resistance
(R).
20.
21. c. The volume (V) of a gas at
constant temperature varies
inversely as the pressure (P).
22.
23. d. The altitude (h) of a
triangle with a constant area
varies inversely as the base
(b).
24.
25. e. The time (t) required to
travel a given fixed distance
is inversely proportional to
the speed (r).
26.
27. Exercise #2.4
Identify whether each of the
following represents an inverse
variation or not. Write IV if it is
inverse variation and write NIV
if not.
