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

If y varies directly with x, and y = 6 when x = 2, what is the value of y when x = 4?

Back

12

Front

The height of a wave in California varies directly with the seconds that pass by. If the wave is 6 feet high at 4 seconds, how high will it be at 10 seconds?

Back

15 feet (using the ratio 6/4 = height/10).

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation.

Front

If y = 150 when x = 2, what is y when x = 25?

Back

1,875 (using the ratio 150/2 = y/25).

Front

If y varies directly with x, and y is 84 when x is 16, what is the constant of variation (k)?

Back

k = 5.25 (since k = y/x = 84/16).

Front

What does the constant of variation (k) represent in direct variation?

Back

The constant of variation (k) represents the rate at which y changes with respect to x.

Front

If y = 5.25x, what is the value of y when x = 10?

Back

52.5

Front

How do you find the value of y when given x in a direct variation equation?

Back

Substitute the value of x into the equation y = kx and solve for y.

Front

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

Back

y = 4x (since k = 12/3 = 4).