Direct and Indirect Variation

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, typically expressed as y = kx, where k is the constant of proportionality.

Front

What is the constant of proportionality in direct variation?

Back

The constant of proportionality is the constant factor (k) that relates the two variables in a direct variation equation.

Front

How can you determine if a table represents direct variation?

Back

A table represents direct variation if the ratio of y to x is constant for all pairs of values.

Front

What is indirect variation?

Back

Indirect variation, also known as inverse variation, is a relationship where one variable increases as the other decreases, typically expressed as y = k/x.

Front

What is the equation for indirect variation?

Back

The equation for indirect variation is y = k/x, where k is a constant.

Front

If y varies inversely with x, what happens to y when x increases?

Back

If y varies inversely with x, y decreases as x increases.

Front

How do you find the constant of variation in indirect variation?

Back

To find the constant of variation in indirect variation, multiply the values of x and y (k = xy) for any pair of corresponding values.

Front

What is an example of a direct variation problem?

Back

An example of a direct variation problem is: If a car travels 60 miles in 1 hour, how far will it travel in 3 hours? (Answer: 180 miles)

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What is an example of an indirect variation problem?

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An example of an indirect variation problem is: If 4 workers can complete a job in 10 hours, how long will it take 2 workers to complete the same job? (Answer: 20 hours)

Front

What does it mean if a relationship does not represent direct variation?

Back

If a relationship does not represent direct variation, it means that the ratio of y to x is not constant.