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 the constant of variation.

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 xy = k, where k is the constant.

Front

How do you identify Direct Variation from a table of values?

Back

If the ratio of y to x is constant for all pairs of values, then it is a direct variation.

Front

How do you identify Inverse Variation from a table of values?

Back

If the product of x and y is constant for all pairs of values, then it is an inverse variation.

Tags

CCSS.HSF-LE.A.1B

Front

What is the constant of variation in Direct Variation?

Back

The constant of variation in Direct Variation is the value of k in the equation y = kx.

Front

What is the constant of variation in Inverse Variation?

Back

The constant of variation in Inverse Variation is the value of k in the equation xy = k.

Tags

CCSS.HSF-LE.A.1B

Front

If y varies directly with x and y = 8 when x = 2, what is the constant of variation?

Back

k = 4 (since y = kx, 8 = k(2) => k = 8/2 = 4).

Front

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

Back

k = 12 (since xy = k, 3(4) = k => k = 12).

Front

Write the equation for a direct variation where k = 5.

Back

y = 5x.

Front

Write the equation for an inverse variation where k = 20.

Back

xy = 20.