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Now, were going to consider an example of proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money well pay.
Students calculate the rate of change also know as the constant of proportionality (k = y/x) which is the constant ratio between two proportional quantities y/x denoted by the symbol k which may be a positive rational number. The x value is directly proportional to the y value such as in the equation y = kx.
In Writing Equations for Proportional Relationships: Word Problems, students will need to determine the constant of proportionality from each word problem, and then write the equation in the form y = kx.
A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor. You can recognize a proportional relationship by looking at data, an equation, or a graph.
To know if a relationship is proportional, you should look at the ratios between the two variables. If the ratio is always the same, the relationship is proportional. If the ratio changes, the relationship is not proportional.
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Example: If a car gets 20 miles to the gallon, how many gallons of gas will it use to travel 180 miles?
When two different values have ratios that are equivalent to one another, we say that a proportional relationship exists between these two variables. If they are points on a graph or a system that can be graphed, we can easily tell how the second variable is going to change if we adjust the first variable.

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