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Ratio is the comparison of two quantities of same kind by division. It can be represented in three ways.
i) Fraction
ii) Using the word "to"
iii) Using a colon
Proportion
A proportion is an equation that states that two ratios are equal.
Proportional Relationship
Definition
If two quantities vary directly with one another, then they are in a proportional relationship.
If one of the quantities is doubled, then the other will also double.
Therefore, the equation of proportional relationships is of the form y = mx.
In order to determine if the graph of a relationship passes through the origin (the point (0, 0)), plug in x = 0 into the given equation and determine the value of y.
The value of y should be 0.
For example, if the fuel usage of a car is described by the equation y = 15x, where y is the amount of fuel used (in gallons) and x is the distance traveled by the car (in miles), then plug in x = 0. This represents the distance traveled by the car as 0 miles.
y = 15(0) = 0
This means when the distance traveled is 0 miles, then 0 gallons of fuel are used.
Therefore, the graph of the equation y = 15x would pass through the point (0, 0) and it is a proportional relationship.
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