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 the constant of variation.

Front

What does the constant of variation (k) represent?

Back

The constant of variation (k) represents the ratio of y to x in a direct variation relationship. It indicates how much y changes for a unit change in x.

Front

If y varies directly with x, what is the slope of the line representing this relationship?

Back

The slope of the line representing a direct variation is equal to the constant of variation (k).

Front

How do you find the constant of variation (k) from a table of values?

Back

To find k, divide the value of y by the corresponding value of x for any pair of values in the table (k = y/x).

Front

If y = 39 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 39/3 = 13.

Front

If $70 is earned in 5 hours, how much is earned in 22 hours?

Back

$308 (Using direct variation: k = 70/5 = 14; then, 14 * 22 = 308).

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx.

Front

If y = 16 when x = 2, what is the value of k?

Back

k = y/x = 16/2 = 8.

Front

In a direct variation, if k = 24, what is y when x = 4?

Back

y = kx = 24 * 4 = 96.

Front

What is the relationship between x and y in direct variation?

Back

In direct variation, as x increases, y increases proportionally, and as x decreases, y decreases proportionally.