Direct, Inverse, & Joint 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 variables is a constant. It can be expressed as xy = k, where k is a non-zero constant.

Front

What is Joint Variation?

Back

Joint Variation is a relationship where a variable varies directly with two or more other variables. It can be expressed as z = kxy, where k is a non-zero constant.

Front

If y varies directly as x and y = 10 when x = 2, what is the value of y when x = 5?

Back

y = 25

Front

If x varies inversely as y and xy = 12, what is the value of y when x = 3?

Back

y = 4

Front

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 5 cm on a side is 250 g, find the weight of the liquid in a cubical container 3 cm on a side.

Back

54 g

Front

What kind of equation is xy = 8?

Back

Inverse Variation

Front

The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. If a wind blowing at 50 mph exerts a force of 75 pounds on a surface of 500 ft², how much force will a wind of 75 mph place on a surface of 10 ft²?

Back

3.375 pounds

Front

Which of the following graphs represents a direct variation?

Back

Graph C

Front

If f varies jointly as q² and h, and f = 96 when q = 4 and h = 3, find q when f = 48 and h = 6.

Back

2