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, typically expressed as y = kx, where k is a non-zero constant.

Front

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

Back

To find the constant of variation (k), divide the value of y by the corresponding value of x (k = y/x).

Front

If y varies directly as x and y = 12 when x = 4, what is the value of k?

Back

k = 12/4 = 3.

Front

In a direct variation equation, what does the variable k represent?

Back

The variable k represents the constant of variation, which indicates how much y changes for a unit change in x.

Front

If a person weighs 80 kg and contains 50 kg of water, what is the constant of variation for water in relation to mass?

Back

k = 50/80 = 0.625.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx.

Front

If y = 20 when x = 5, what is the value of y when x = 10 in a direct variation?

Back

y = kx; k = 20/5 = 4; when x = 10, y = 4 * 10 = 40.

Front

How can you determine if two quantities vary directly?

Back

Two quantities vary directly if their ratio remains constant as the values change.

Front

What is the relationship between the number of hours worked and earnings in a direct variation scenario?

Back

In a direct variation scenario, earnings increase proportionally with the number of hours worked.

Front

If a dishwasher uses 65 gallons of water for 5 loads, how many gallons does it use per load?

Back

Gallons per load = 65 gallons / 5 loads = 13 gallons per load.