Direct Variation Practice

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 the constant of variation.

Front

What is the constant of variation in direct variation?

Back

The constant of variation (k) is the ratio of y to x in a direct variation relationship, represented as k = y/x.

Front

If y varies directly with x and y = 8 when x = 4, what is the constant of variation?

Back

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

Front

Which equation represents a direct variation relationship?

Back

The equation y = kx, where k is a non-zero constant.

Front

If y varies directly with x and y = 12 when x = 3, what is the value of y when x = 6?

Back

y = kx; k = 12/3 = 4; y = 4 * 6 = 24.

Front

What is the equation of direct variation if y varies directly with x and k is the constant of variation?

Back

The equation is y = kx.

Front

If y varies directly with x and y = 16 when x = 32, what is the equation representing this situation?

Back

k = y/x = 16/32 = 1/2; the equation is y = (1/2)x.

Front

How do you find the constant of variation from a direct variation equation?

Back

To find k, rearrange the equation y = kx to k = y/x.

Front

What is an example of a direct variation equation?

Back

An example is y = 3x, where the constant of variation k = 3.

Front

If y = 5 when x = 10, what is the constant of variation?

Back

k = y/x = 5/10 = 1/2.