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 the constant of variation.

Front

What does the constant of variation (k) represent?

Back

The constant of variation (k) represents the ratio of the two variables in a direct variation relationship. It indicates how much one variable changes in relation to the other.

Front

If y varies directly with x, what is the equation form?

Back

The equation form is y = kx, where k is the constant of variation.

Front

How can you identify a direct variation graph?

Back

A direct variation graph is a straight line that passes through the origin (0,0).

Front

If $70 is earned in 5 hours, how much is earned in 22 hours?

Back

$308

Front

What is the equation for the relationship if y = 3x?

Back

This equation indicates that for every unit increase in x, y increases by 3 units.

Front

What is the constant of variation if a dishwasher uses 65 gallons of water for 5 loads?

Back

k = 13 (because 65 gallons / 5 loads = 13 gallons per load).

Front

If lightning is seen and thunder is heard 10 seconds later, and the lightning is 2 miles away, what is the equation of variation?

Back

y = 5x (where y is the distance in miles and x is the time in seconds).

Front

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

Back

The amount of money earned is directly proportional to the number of hours worked.

Front

What does it mean if two quantities vary directly?

Back

It means that as one quantity increases, the other quantity increases at a constant rate.