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

If y varies directly as x, and y = 12 when x = 15, what is the constant of variation (k)?

Back

To find k, use the formula k = y/x. Here, k = 12/15 = 0.8.

Front

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

Back

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

Front

In a direct variation problem, if the constant of variation is 5, what is the value of y when x = 10?

Back

y = kx = 5 * 10 = 50.

Front

What is the relationship between the variables in a direct variation?

Back

In direct variation, as one variable increases, the other variable also increases, and vice versa.

Front

If 4 apples cost $0.45, what is the cost of 1 apple?

Back

The cost of 1 apple is $0.45 / 4 = $0.1125.

Front

If the number of hours worked is directly proportional to the earnings, how would you express this relationship mathematically?

Back

Earnings = k * Hours, where k is the rate of earnings per hour.

Front

In a direct variation, if y = 6 when x = 27, what is the value of y when x = 2?

Back

Using the constant of variation k = 6/27, y = (6/27) * 2 = 0.444.

Front

What is the formula to convert feet to yards in a direct variation scenario?

Back

Yards = (Feet / 3) * 30, based on the given relationship.

Front

If a store earns $11,500 in 4 hours, how much will it earn in 8 hours?

Back

It will earn $23,000, as it is a direct variation.