Direct and Inverse Variation Concepts

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.

Front

If y varies directly with x and y = 84 when x = 16, what is the constant of variation (k)?

Back

k = y/x = 84/16 = 5.25.

Front

If y varies inversely with x and y = 150 when x = 2, what is the equation representing this relationship?

Back

y = 300/x.

Front

How do you find y when y varies inversely with x and you know y = 150 when x = 2?

Back

Use the equation y = k/x. First, find k: k = y * x = 150 * 2 = 300. Then, for x = 25, y = 300/25 = 12.

Front

What is the equation for direct variation?

Back

The equation for direct variation is y = kx.

Front

What is the equation for inverse variation?

Back

The equation for inverse variation is y = k/x.

Front

If the width of a rectangle varies inversely with its length and the width is 6 when the length is 24, what is the equation?

Back

y = 144/x.

Front

In direct variation, if y = 5.25x, what is the value of y when x = 10?

Back

y = 5.25 * 10 = 52.5.

Front

If a person with a mass of 90 kg contains 60 kg of water, how much water is in a person with a mass of 75 kg?

Back

50 kg of water.