direct and indirect variations

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 y varies directly with x and y = 10 when x = 5, what is the constant of variation, k?

Back

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

Front

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

Back

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

Front

How do you determine if a table represents direct variation?

Back

A table represents direct variation if the ratio of y to x is constant for all pairs of values.

Front

How do you determine if a table represents inverse variation?

Back

A table represents inverse variation if the product of x and y is constant for all pairs of values.

Front

If y = 3 when x = 9, what is 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, what is y when x = 6 in inverse variation?

Back

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