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

What is the unit rate?

Back

The unit rate is a comparison of two different quantities when they are combined together. It is often expressed as a quantity per one unit of another quantity.

Front

If y varies directly with x, what does that mean?

Back

It means that as x increases or decreases, y changes in a proportional manner. The ratio y/x remains constant.

Front

How do you find the constant of variation (k) in direct variation?

Back

To find k, divide y by x (k = y/x) when you have values for both variables.

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 = 12 when x = 15, what is the constant of variation (k)?

Back

k = y/x = 12/15 = 0.8.

Front

If y = 39 when x = 3, what is y when x = 2?

Back

y = kx; k = 39/3 = 13. Therefore, y = 13 * 2 = 26.

Front

How do you solve for y when given x in a direct variation problem?

Back

Use the formula y = kx, substituting the value of k and the given x.

Front

What is the relationship between hours worked and pay in direct variation?

Back

In direct variation, pay is directly proportional to the number of hours worked, meaning if hours increase, pay increases at a constant rate.

Front

If Shawn earns $123 for 20 hours, how much does he earn per hour?

Back

To find the hourly rate, divide total pay by hours: $123/20 = $6.15 per hour.