Understanding Direct Variation | Exploring Mathematical Relationships with Proportional Changes

direct variation

Direct variation is a mathematical relationship between two variables in which their values always change proportionally

Direct variation is a mathematical relationship between two variables in which their values always change proportionally. This means that as one variable increases (or decreases), the other variable also increases (or decreases) by a constant factor. In direct variation, the ratio between the two variables remains constant.

Mathematically, if we have two variables x and y, we say that y varies directly with x if there exists a constant k such that:

y = kx

In this equation, k represents the constant of variation, which represents the ratio between the values of y and x.

For example, let’s consider a situation where the number of hours worked by a person is directly related to their earnings. If we let x represent the number of hours worked and y represent the earnings, we can write the direct variation equation:

earnings = k * hours

Here, the constant of variation (k) represents the hourly wage of the person. So, if the hourly wage is $10, the equation becomes:

earnings = 10 * hours

In this case, the earnings and the number of hours worked are in direct variation, as the earnings increase linearly with the number of hours worked with a constant rate of $10 per hour.

To determine if two variables are in direct variation, you can check if the ratio between them remains constant. If the ratio is consistent for different values of x and y, then they are in direct variation.

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