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.

Front

If y varies directly with x and y = 10 when x = 2, what is the constant of variation?

Back

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

Front

If y = 5.25x, what is the value of y when x = 4?

Back

y = 5.25 * 4 = 21.

Front

What is the equation for inverse variation if y = 12 when x = 3?

Back

k = y * x = 12 * 3 = 36, so y = 36/x.

Front

How do you find the constant of variation in direct variation?

Back

The constant of variation (k) is found by dividing y by x (k = y/x).

Front

In a direct variation, if y = 39 when x = 3, what is y when x = 6?

Back

y = kx; k = 39/3 = 13, so y = 13 * 6 = 78.

Front

What does the equation y = k/x represent?

Back

This equation represents inverse variation, where y decreases as x increases.

Front

If y varies directly with x and y = 84 when x = 16, what is the equation?

Back

y = 5.25x.

Front

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

Back

In inverse variation, as one variable increases, the other decreases, keeping the product constant.