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.

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.

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.