Direct & Inverse 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. It can be expressed as y = kx, where k is a non-zero constant.

Front

What is Inverse Variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as y = k/x, where k is a non-zero constant.

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How can you identify Direct Variation from a graph?

Back

In a graph of direct variation, the line passes through the origin (0,0) and has a positive slope.

Front

How can you identify Inverse Variation from a graph?

Back

In a graph of inverse variation, the curve approaches the axes but never touches them, indicating that as one variable increases, the other decreases.

Tags

CCSS.8.EE.B.5

Front

What is the equation for Direct Variation?

Back

The equation for direct variation is y = kx, where k is the constant of variation.

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What is the equation for Inverse Variation?

Back

The equation for inverse variation is y = k/x, where k is the constant of variation.

Front

If y varies directly with x and y = 10 when x = 2, what is the constant of variation?

Back

The constant of variation k = y/x = 10/2 = 5.

Front

If y varies inversely with x and y = 4 when x = 3, what is the constant of variation?

Back

The constant of variation k = y * x = 4 * 3 = 12.

Front

What does it mean if two variables are directly proportional?

Back

If two variables are directly proportional, it means that as one variable increases, the other variable also increases at a constant rate.

Tags

CCSS.HSF-LE.A.1B

Front

What does it mean if two variables are inversely proportional?

Back

If two variables are inversely proportional, it means that as one variable increases, the other variable decreases, such that their product remains constant.