Direct Variation Flashcard

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

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

Back

To find the constant of variation (k), divide y by x (k = y/x) when given a pair of values.

Front

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

Back

k = y/x = 12/3 = 4.

Front

Write the equation of direct variation if y = 5 when x = 2.

Back

y = 2.5x.

Front

If the width of a rectangle varies directly with its length, and the width is 6 when the length is 24, what is the equation?

Back

y = 0.25x.

Front

If y varies directly with x, and y = 24 when x = 6, what is the value of y when x = 12?

Back

y = 48.

Front

The height of a wave varies directly with time. If the wave is 6 feet high at 4 seconds, what is the height at 10 seconds?

Back

y = 15 feet.

Front

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

Back

y = 5.25x.

Front

How do you solve for y in a direct variation problem?

Back

Use the equation y = kx, substituting the known values to find y.

Front

If a person with a mass of 90 kg contains 60 kg of water, how much water is in a person with a mass of 75 kg?

Back

50 kg of water.