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

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

How do you find the value of y when x is given in a direct variation?

Back

Use the formula y = kx, where k is the constant of variation.

Front

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

Back

$70 / 5 hours = $14 per hour.

Front

If a person earns $14 per hour, how much will they earn in 22 hours?

Back

Earnings = 14 * 22 = $308.

Front

What is the formula to calculate earnings based on hours worked in direct variation?

Back

Earnings = (Earnings per hour) * (Number of hours worked).

Front

If Trina earns $187.15 for 19 hours, how do you find her earnings for 40 hours?

Back

First, find her earnings per hour: $187.15 / 19 hours = $9.85 per hour. Then, multiply by 40 hours: 9.85 * 40 = $394.

Front

In a direct variation, if a person with a mass of 90 kg contains 60 kg of water, what is the constant of variation?

Back

k = 60 kg / 90 kg = 0.67 kg of water per kg of mass.

Front

How do you find the amount of water in a person with a mass of 75 kg?

Back

Water = k * mass = 0.67 * 75 = 50 kg.

Front

If Shawn earns $123 for 20 hours, what is his pay rate per hour?

Back

Pay rate = $123 / 20 hours = $6.15 per hour.