Download Unit 3: Ratios and Proportional Relationships

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Proportional Relationships
There are three ways to represent proportional relationships: table, graph and an
equation.
Constant of Proportionality:
Equation
𝑦
= 𝑘
𝑥
y= kx
k is the constant of proportionality.
Also known as a unit rate or unit price. It is
comparing a quantity to one single unit of
another quantity.
y is the dependent variable (output)
x is the independent variable (input)
Table
Graph
A table is in proportion if you get a constant of
proportionality when you divide the two
numbers.
A graph is proportional if it is a straight line
and goes through the origin.
X (input)
Y (output)
0
0
1
3
2
6
3
9
By manipulating the formula to find the constant of proportionality, you get the
equation.
𝑦
= 𝑘
𝑥
(𝑥)
𝑦
= 𝑘(𝑥)
𝑥
𝑦 = 𝑘𝑥
A table shows multiple equivalent ratios. To test to see if the table is proportional,
you divide y by x and see if they are all equal. If they are all equal, then the number is the
constant of proportionality. With the table being arranged as a comparison of x to y, it
lends itself to creating a graph.
A graph has to have two characteristics of being a straight line and goes through the
origin. Both of these characteristics need to be on the graph. With a graph of the
proportional relationship you can see the unit rate at (1,r) r is the same as the constant
of proportionality. In the above example, you can see how the graph is straight, includes
the origin (0,0) and has a constant of proportionality 3 by looking at (1,3).