Understanding Proportionality
Testing for Proportionality
Algebraically
You can test proportionality by using cross products.
Graphically
Plot points on a graph and observe if the graph is a
straight line through the origin.
Hours
0
1
2
3
4
Water
(gallon)
0
5
10
15
20
Types of Ratios & Proportions
Part to Part
Part to Whole
There are 18 girls and 12 boys in Ms. Smith’s
class. There are 42 girls and 30 boys in the
Band. Is the ratio of girls to boys in Ms. Smith’s
class proportional to the girls to boys in band?
There are 240 7th graders and 48 of them are
left handed. In Ms. Jones class of 30 students, 6
of them are left handed. Is the ratio of left
handed students in Ms. Jones class proportional
to the entire 7th grade class?
𝟏𝟖
𝟏𝟐
≠
𝟒𝟐
𝟑𝟎
→ NO
𝟔
𝟑𝟎
=
𝟒𝟖
𝟐𝟒𝟎
→ YES
Recognizing the Constant of Proportionality
in a ….
Table
Hours
(x)
1
2
3
4
5
Water
(gallon)
(y)
5
10
15
20
25
A table
represents a
proportion if
the ratio of
the change in
x to the
change in y is
constant
Graph
Equation
y = kx
k represents
the constant of
proportionality
A graph
represents a
proportion if the
points form a
straight line that
passes through
the origin.
y = 7x
y = 0.5x
𝟏
y= x
𝟒
An equation
represents a
proportion when
one variable in a
direct variation
increases, the
other variable also
increases.
Verbal
Description
A plumber is
paid hourly. The
more hours
worked, the
more the
plumber is paid.
A verbal
description
represents a
proportion if it has
two quantities that
vary at the same
rate and the ratio
between the
quantities is
constant.
$𝟏𝟎𝟎
$𝟓𝟎
𝟐 𝐡𝐫
= 𝟏 𝐡𝐫
$𝟕𝟎𝟎
$𝟓𝟎
=
𝟏𝟒 𝒉𝒓 𝟏 𝐡𝐫