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 in the form y = kx, where k is a non-zero constant.

Front

What does the equation y = 2x represent?

Back

This equation represents a direct variation where y varies directly with x, and the constant of variation (k) is 2.

Front

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

Back

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

Front

How do you find the value of y when x = 2 if y varies directly with x and k = 13?

Back

y = kx = 13 * 2 = 26.

Front

What is the equation for a direct variation if y = 3 when x = 1?

Back

The equation is y = 3x.

Front

If y = 4x, what is the value of y when x = 5?

Back

y = 4 * 5 = 20.

Front

What is the relationship between x and y in the equation y = 1/4x?

Back

y varies directly with x, and the constant of variation is 1/4.

Front

If a tutor earns $222 for 10 hours of work, how much do they earn per hour?

Back

They earn $222 / 10 = $22.20 per hour.

Front

If y = 3x, what is y when x = 4?

Back

y = 3 * 4 = 12.

Front

What does it mean if a relationship is not a direct variation?

Back

It means that the relationship between the variables cannot be expressed in the form y = kx, where k is a constant.