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Does the relationship between x and y represent direct or inverse variation? What is the constant of variation?

User Entalyan
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Final Answer:

The relationship between x and y represents direct variation. The constant of variation is represented by the ratio of y to x.

Step-by-step explanation:

In direct variation, two variables, in this case, x and y, are related in such a way that as one variable increases, the other also increases proportionally. Mathematically, this can be expressed as y = kx, where "k" is the constant of variation. To determine the nature of the variation, we can observe the given relationship between x and y.

If the relationship is direct, it means that as x increases, y also increases, and vice versa. In this scenario, the constant of variation (k) can be found by taking the ratio of any pair of corresponding values of x and y. Let's denote two points on the relationship as (x1, y1) and (x2, y2). The constant of variation is given by k = y1/x1 = y2/x2.

Upon analyzing the relationship between x and y, we can observe that the constant ratio between corresponding values holds true. Therefore, the relationship between x and y is direct, and the constant of variation is the same for all pairs of values.

User Henrik Ilgen
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