direct variation
The relationship between two variable quantities that have a constant ratio.
Direct variation is a type of relationship between two variables in which one variable increases or decreases proportionally with the changes in the other variable. In direct variation, the ratio of the two variables remains constant, meaning that if one variable doubles, the other variable will also double.
A common equation used to express direct variation is y = kx, where y and x are the two variables and k is the constant of proportionality. This means that as x increases, y will increase proportionally by a factor of k and vice versa.
For example, if y represents the cost of buying x items and k is the cost per item, we can say that this is a direct variation. If the cost per item is $10, then the equation would be y = 10x. This means that if you buy 2 items, the cost would be $20, and if you buy 5 items, the cost would be $50, which shows the constant ratio of 10:1.
Direct variation is often used to solve problems in physics, chemistry, and other sciences where the two variables are related in a proportional way. It is also commonly used in mathematics to solve problems involving proportions, rates, and ratios. Overall, understanding direct variation helps to simplify mathematical problems and make them easier to solve.
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