Basic Variation Patterns (p. 6)
Direct Variation: _______ or ______
y varies directly with x
y is directly proportional to x
for some constant k (constant of proportionality)
All of these mean:
________________________________________
________________________________________
The ratio of y to x is constant.
Ex:
Ex:
7. Explain why the perimeter P of a square is directly proportional to the length s of a side.
s
a. Direct variation equation:
s
s
b. Constant of proportionality:
c. As the value of s increases, P…..
s
How is this pattern related to the constant of proportionality?
8. There are two relationships from Problem 5 that are direct variations. Find these two and fill
in the chart, one column per relationship.
Direct variation relationships
(brief description of function)
a. How does the dependent
variable change as the
independent variable increases?
b. Fill in the blanks:
c. Relationship in an equivalent
symbolic form.
The variable ______________is
directly proportional to
________________, with
constant or proportionality _____.
The variable ______________is
directly proportional to
________________, with
constant or proportionality _____.
Inverse Variation: ______ or ________ for some constant k (constant of proportionality)
y varies inversely as x
All of these mean:
________________________________________
________________________________________
y is inversely proportional to x
The product of y to x is constant.
Ex:
Ex:
9. Time t required to download a 4-megabyte music file on the internet is inversely proportional
to the rate r at which the data is transferred.
a. time it takes to download a 4-megabyte file if the transfer rate is 2.5 megabytes per minute….
if the transfer rate is 0.8 megabytes per minute……
b. symbolic form for relationship between t and r……
c. As r increases, t……..
How is this pattern related to the constant of proportionality?
In our experiments with ramp height, platform length, and roll time, what were the constants of
each?
a. Ramp Length vs. Roll Time:
b. Platform Height vs. Roll Time:
6. Using your graphs (data plots) from Problems 2 and 3 and your new knowledge of direct and
inverse variation, can you find function rules that might be good models for the relationships
between (make sure you label what your constant is in the context of each graph):
a. roll time T and ramp length L:
b. roll time T and platform height H:
Substitute in the corresponding table values for k in your above equations. Do your equations
match the data closely? Explain.
10. There are two relationships from Problem 5 that are inverse variations. Find these two and
fill in the chart, one column per relationship.
Inverse variation relationships
(brief description of function)
How does the dependent
variable change as the
independent variable increases?
Relationship in two different
equivalent symbolic forms.
Fill in the blanks:
The variable _____________is
inversely proportional to
________________, with
constant or proportionality _____.
The variable _____________is
inversely proportional to
________________, with
constant or proportionality _____.
11. For the tables given, check whether the relationship is direct or inverse variation and give the
constant of proportionality.
Table
I
II
III
Direct?
Inverse?
Constant of
Proportionality