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 non-zero 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 non-zero constant.

Front

If y varies inversely with x, and y = 4 when x = 7, what is the constant of variation (k)?

Back

k = xy = 4 * 7 = 28.

Front

If y = 28/x, what is y when x = 2?

Back

y = 28/2 = 14.

Front

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

Back

y = (10/5) * 10 = 20.

Front

What type of variation is represented by the equation y = 10/x?

Back

Inverse variation.

Front

If both quantities are increasing, what type of variation is it?

Back

Direct variation.

Front

If y = k/x, what happens to y as x increases?

Back

y decreases.

Front

If y = kx, what happens to y as x decreases?

Back

y decreases.

Front

What is the relationship between x and y in inverse variation?

Back

As one variable increases, the other variable decreases.