Direct and 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 xy = k, where k is a non-zero constant.

Front

If y varies directly as x and y = 10 when x = 2, what is the constant of variation (k)?

Back

k = y/x = 10/2 = 5.

Front

If y varies inversely as x and y = 8 when x = 4, what is the constant of variation (k)?

Back

k = xy = 8 * 4 = 32.

Front

What is the equation for direct variation?

Back

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

Front

What is the equation for inverse variation?

Back

The equation for inverse variation is xy = k, where k is the constant.

Front

If y = 3 when x = 9, find y when x = 3 in direct variation.

Back

y = kx; k = 3/9 = 1/3; y = (1/3) * 3 = 1.

Front

If y = 12 when x = 3, find y when x = 6 in inverse variation.

Back

xy = k; k = 12 * 3 = 36; y = 36/6 = 6.

Front

What does it mean if two variables vary directly?

Back

It means that as one variable increases, the other variable also increases, and vice versa.

Front

What does it mean if two variables vary inversely?

Back

It means that as one variable increases, the other variable decreases, and vice versa.