Question

Is the relationship between the values in the table to the right a direct variation, an inverse variation, or neither? If the relationship is a direct or inverse variation, then write an equation to model the variation.

Answer 1

The relationship represents an inverse variation; as x values increase, y values decrease.

What is meant by inverse variation?

• Inverse variation is a relationship between two variables in which the value of one increases while the value of the other decreases. If y varies inversely as x and x = 5 when y = 2, the constant of variation is k = xy = 5(2) = 10. As a result, the equation for this inverse variation is xy = 10.

• In contrast to direct variation, which describes a linear relationship between two variables, inverse variation describes a different type of relationship.

• When two quantities have inverse variation, as one increases, the other decreases.

• When the ratio x:y remains constant, two values x and y are said to be directly proportional to each other.

Therefore,

In the formula y = mx + b,

Given

y = 24, 12, 8, 6 and x = 4, 8, 12, 16

Let the equation be y = k/x

substitute the values in the above equation, we get

24 = k/4

simplifying the above equation, we get

k = 24 × 4

k = 96

y = k/x

substitute the values in the above equation, we get

12 = k/8

simplifying the above equation, we get

k = 12 × 8

k = 96

Therefore k = 96

To learn more about inverse variation, refer to:

brainly.com/question/13998680

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