Direct and Inverse 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 is inverse variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as y = k/x, where k is the constant of variation.

Front

If y varies directly as x and y = 15 when x = 12, what is the constant of variation (k)?

Back

k = y/x = 15/12 = 1.25.

Front

If Trina earns $187.15 for 19 hours of work, how much will she earn for 40 hours?

Back

$394.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx.

Front

What is the formula for inverse variation?

Back

The formula for inverse variation is y = k/x.

Front

If y = 3 when x = 1, what is y when x = 4 in direct variation?

Back

y = kx; k = 3. So, y = 3(4) = 12.

Front

In the equation y = k/x, what does k represent?

Back

k represents the constant of variation in inverse variation.

Front

How do you determine if a table represents direct variation?

Back

A table represents direct variation if the ratio of y to x is constant for all pairs of values.

Front

If the height of a wave varies directly with time and is 6 feet at 4 seconds, how high is it at 6.6 seconds?

Back

10 feet.