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 does the equation y = kx represent?

Back

The equation y = kx represents direct variation, where y varies directly with x, and k is the constant of variation.

Front

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

Back

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

Front

If y varies directly with x and y = 12 when x = 15, what is the value of k?

Back

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

Front

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

Back

To find y, use the formula y = kx, substituting the value of k and the given x.

Front

If a person with a mass of 90 kg contains 60 kg of water, what is the constant of variation for water in relation to mass?

Back

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

Front

How many kilograms of water are in a person whose mass is 75 kg if the constant of variation is 0.67?

Back

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

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.

Front

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

Back

Earnings per hour = $123 / 20 hours = $6.15 per hour.

Front

If Shawn works 31 hours, how do you calculate his pay?

Back

Pay = hourly rate * hours worked = $6.15 * 31 = $190.65.