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 = 84 when x = 16, what is the constant of variation (k)?

Back

k = \frac{y}{x} = \frac{84}{16} = 5.25.

Front

Write the equation for direct variation when y = 6 and x = 24.

Back

y = 0.25x.

Front

How do you determine if an equation represents direct variation?

Back

An equation represents direct variation if it can be written in the form y = kx, where k is a non-zero constant. If there is an added or subtracted constant, it is not direct variation.

Front

If y varies directly with x and y = 150 when x = 2, what is y when x = 25?

Back

y = kx; k = \frac{150}{2} = 75. Therefore, y = 75 \times 25 = 1875.

Front

Is the equation y = 2x + 1 a direct variation?

Back

No, because it includes a constant term (+1) which prevents it from being in the form y = kx.

Front

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

Back

Using the constant of variation, k = \frac{6}{4} = 1.5. Therefore, height at 10 seconds = 1.5 \times 10 = 15 feet.

Front

What is the formula to find the constant of variation (k) in direct variation?

Back

k = \frac{y}{x}.

Front

If y varies directly with x and k = 3, what is the equation?

Back

y = 3x.

Front

If y = 12 when x = 4, what is the constant of variation?

Back

k = \frac{12}{4} = 3.