8.5E Direct Variation Homework

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

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

Back

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

Front

In a direct variation, if x is halved, what happens to y?

Back

y is also halved.

Front

If y = kx and k = 5, what is y when x = 4?

Back

y = 5 * 4 = 20.

Front

Trina earns $187.15 for 19 hours of work. How much does she earn per hour?

Back

Earnings per hour = $187.15 / 19 hours = $9.85.

Front

If Trina works 40 hours, how much will she earn?

Back

Earnings = 40 hours * $9.85/hour = $394.

Front

A person with a mass of 90 kg contains 60 kg of water. What is the ratio of water to mass?

Back

Ratio = 60 kg water / 90 kg mass = 2/3.

Front

If a person weighs 75 kg, how much water do they contain based on the ratio?

Back

Water = (2/3) * 75 kg = 50 kg.

Front

Shawn earns $123 for 20 hours of work. What is his hourly wage?

Back

Hourly wage = $123 / 20 hours = $6.15.

Front

How much will Shawn earn for 31 hours of work?

Back

Earnings = 31 hours * $6.15/hour = $190.65.