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Proportional relationship
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GPT 3.5
A proportional relationship is a mathematical relationship between two variables in which they change in a consistent and predictable way. In a proportional relationship, when one variable increases, the other variable also increases by a corresponding amount, and when one variable decreases, the other variable also decreases by a corresponding amount.
Mathematically, if two variables x and y have a proportional relationship, it can be expressed as y = kx, where k is a constant called the constant of proportionality. This equation means that for every increase in x, there is a corresponding increase in y that is directly proportional to the constant of proportionality.
For example, if a car is driving at a constant speed, the distance traveled and the time elapsed have a proportional relationship. If the car is traveling at a constant speed of 60 miles per hour, the distance traveled in x hours can be expressed as y = 60x, indicating a proportional relationship.
In a proportional relationship, the graph of the relationship will always pass through the origin (0,0) and will be a straight line. The slope of the line represents the constant of proportionality, and it indicates how much y increases for each unit increase in x.
Proportional relationships are important in various fields, including physics, economics, and finance, where they can be used to analyze and predict how variables are related to each other.
Mathematically, if two variables x and y have a proportional relationship, it can be expressed as y = kx, where k is a constant called the constant of proportionality. This equation means that for every increase in x, there is a corresponding increase in y that is directly proportional to the constant of proportionality.
For example, if a car is driving at a constant speed, the distance traveled and the time elapsed have a proportional relationship. If the car is traveling at a constant speed of 60 miles per hour, the distance traveled in x hours can be expressed as y = 60x, indicating a proportional relationship.
In a proportional relationship, the graph of the relationship will always pass through the origin (0,0) and will be a straight line. The slope of the line represents the constant of proportionality, and it indicates how much y increases for each unit increase in x.
Proportional relationships are important in various fields, including physics, economics, and finance, where they can be used to analyze and predict how variables are related to each other.