Direct 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

If y varies directly as x, and y = 4 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 4/3.

Front

If y = kx and k = 2, what is the value of y when x = 5?

Back

y = 2 * 5 = 10.

Front

If y = 12 when x = 4, what is the value of y when x = 6 in a direct variation?

Back

y = (12/4) * 6 = 18.

Front

Which equation represents a direct variation? y = 3x + 2 or y = 3x?

Back

y = 3x represents a direct variation.

Front

If y = -3 when x = 1, what is the value of y when x = -2?

Back

y = -3 * -2 = 6.

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 = 5 when x = 2, what is the value of y when x = 10?

Back

y = (5/2) * 10 = 25.

Front

If y varies directly as x and y = 0 when x = 0, what can be said about the relationship?

Back

The relationship is still a direct variation, as both y and x are zero.

Front

If y = 8 when x = 4, what is the value of k?

Back

k = y/x = 8/4 = 2.