Direct Variation Flashcard

Front

If y varies directly with x, what is the relationship between y and x?

Back

y = kx, where k is the constant of 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.

Front

If y = 6 when x = 2, what is the constant of variation (k)?

Back

k = y/x = 6/2 = 3.

Front

If y varies directly with x and k = 3, what is y when x = 4?

Back

y = kx = 3 * 4 = 12.

Front

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

Back

No, because it includes a constant term (1) that does not vary with x.

Front

If y = 22.5 when x = 15, what is the constant of variation (k)?

Back

k = y/x = 22.5/15 = 1.5.

Front

If y varies directly as x, and y = 30 when x = 20, what is y when x = 10?

Back

y = kx; k = 30/20 = 1.5; y = 1.5 * 10 = 15.

Front

What equation represents the direct variation if y = 84 when x = 16?

Back

y = 5.25x.

Front

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

Back

y = kx; k = 150/2 = 75; y = 75 * 25 = 1875.

Front

How do you determine if a relationship is a direct variation?

Back

Check if the ratio y/x is constant for all values.