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 a non-zero constant.

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 a non-zero constant.

Front

If y varies directly with x and y = 12 when x = 3, what is the equation of variation?

Back

y = 4x.

Front

If y varies inversely with x and y = 3 when x = 6, what is the equation of variation?

Back

y = 18/x.

Front

What is the constant of variation in direct variation?

Back

The constant of variation in direct variation is the ratio of y to x, denoted as k.

Front

What is the constant of variation in inverse variation?

Back

The constant of variation in inverse variation is the product of x and y, denoted as k.

Front

If the height of a wave varies directly with time and is 8 feet at 2 seconds, how high is the wave at 5 seconds?

Back

20 feet.

Front

If the width of a rectangle varies inversely with its length and the width is 10 when the length is 5, what is the equation?

Back

y = 50/x.

Front

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

Back

To find the constant of variation for direct variation, divide y by x (k = y/x).

Front

How do you find the constant of variation for inverse variation?

Back

To find the constant of variation for inverse variation, multiply x and y (k = xy).