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 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 y = k/x, where k is the constant of variation.

Front

If m varies directly as p and m = 35 when p = 5, what is the constant of variation (k)?

Back

k = m/p = 35/5 = 7.

Front

If m varies directly as p, find m when p = 6 if m = 35 when p = 5.

Back

m = k * p = 7 * 6 = 42.

Front

What is the constant (k) in the inverse variation equation y = 400/x?

Back

k = 400.

Front

The frequency of a vibrating string varies inversely as its length. If a 3-foot string vibrates 175 cycles per second, what is the frequency of a 5-foot string?

Back

Frequency = k/length; k = 3 * 175 = 525; Frequency for 5 feet = 525/5 = 105 cycles.

Front

Does the equation y = 2x + 3 represent direct variation?

Back

No, because it includes a constant term (3) that prevents it from being a direct variation.

Front

What type of variation does the equation y = 5/x represent?

Back

Inverse variation.

Front

What is the relationship between the variables in direct variation?

Back

As one variable increases, the other variable also increases, and vice versa.

Front

What is the relationship between the variables in inverse variation?

Back

As one variable increases, the other variable decreases.