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 is the constant of variation in the equation y = kx?

Back

The constant of variation (k) is the ratio of y to x in a direct variation relationship. It remains constant for all values of x and y.

Front

If y = 12 when x = 2, what is the constant of variation?

Back

k = 6

Front

If y = 20 when x = 4, what is y when x = -2?

Back

y = -10

Front

How do you find the unit rate from a total cost?

Back

To find the unit rate, divide the total cost by the number of units. For example, if $3.60 is for 3 pounds, the unit rate is $3.60 / 3 = $1.20 per pound.

Front

If y = -4 when x = -1, what is the constant of variation?

Back

k = 4

Front

What does it mean if a quantity varies directly with another?

Back

It means that as one quantity increases or decreases, the other quantity does so in a proportional manner.

Front

If $240 is earned in 16 hours, how much is earned in a 40-hour work week?

Back

$600

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation.

Front

How can you determine if two quantities are in direct variation?

Back

Two quantities are in direct variation if their ratio is constant, meaning k = y/x is the same for all pairs of values.