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Now, we're 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 we'll pay.
The graph of a linear equation is a line. If b = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x. If b \u2260 0, then y = mx + b is a non-proportional linear relationship between y and x.
You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are all the same, the table shows a proportional relationship.
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant. The proportionality constant's value is determined by the proportion between the two specified quantities.