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 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 the width of a rectangle varies inversely with its length, and the width is 4 when the length is 8, what is the equation representing this relationship?

Back

y = 32/x, where y is the width and x is the length.

Front

What is the constant of variation in the equation y = 3x?

Back

The constant of variation is 3.

Front

How do you determine if a table of values represents direct variation?

Back

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

Front

If y = 12 when x = 4, what is the value of y when x = 6 in a direct variation?

Back

y = kx; k = 12/4 = 3; y = 3 * 6 = 18.

Front

What does it mean if two quantities vary inversely?

Back

It means that as one quantity increases, the other quantity decreases, such that their product remains constant.

Front

In the equation y = k/x, what does k represent?

Back

k represents the constant of variation in inverse variation.

Front

If the interest earned on a savings account varies directly with the amount deposited, what is the formula to calculate interest?

Back

Interest = k * Amount Deposited, where k is the constant of variation.