8.1 Direct, Inverse Variations

Front

What is Direct Variation?

Back

Direct Variation is a relationship between two variables where an increase in one variable results in a proportional increase in the other variable. It can be expressed as y = kx, where k is a constant.

Front

What is Inverse Variation?

Back

Inverse Variation is a relationship between two variables where an increase in one variable results in a proportional decrease in the other variable. It can be expressed as y = k/x, where k is a 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 = 32 when x = 3, what is the equation representing this relationship?

Back

y = k/x, where k = 32 * 3 = 96, so y = 96/x.

Front

What happens to y when x increases in a direct variation?

Back

In direct variation, as x increases, y also increases.

Front

What happens to y when x increases in an inverse variation?

Back

In inverse variation, as x increases, y decreases.

Front

Identify the type of variation: y = 4/21x.

Back

Direct Variation.

Front

Identify the type of variation: y = 96/x.

Back

Inverse Variation.

Front

If y varies directly with x and y = 5 when x = 1, what is y when x = 4?

Back

y = 5 * 4 = 20.

Front

If y varies inversely with x and y = 10 when x = 2, what is y when x = 5?

Back

y = k/x, where k = 10 * 2 = 20, so y = 20/5 = 4.