Direct and inverse variation word problems

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 is inverse variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as y = k/x, where k is a non-zero constant.

Front

How do you write the equation for direct variation?

Back

The equation for direct variation can be written as y = kx, where k is the constant of variation.

Front

How do you write the equation for inverse variation?

Back

The equation for inverse variation can be written as y = k/x, where k is the constant of variation.

Front

If y varies directly with x and y = 10 when x = 2, what is the constant of variation k?

Back

k = y/x = 10/2 = 5.

Front

If y varies inversely with x and y = 4 when x = 3, what is the constant of variation k?

Back

k = y * x = 4 * 3 = 12.

Front

What is the formula to find the cost of gas if it varies directly with the number of gallons purchased?

Back

Cost = k * gallons, where k is the cost per gallon.

Front

If Karen earns $28.50 for working 6 hours, how much does she earn per hour?

Back

She earns $28.50 / 6 = $4.75 per hour.

Front

If the time t varies inversely with speed s, and t = 40 minutes at s = 9 mph, how do you find t at s = 12 mph?

Back

Use the formula t = k/s. First, find k: k = t * s = 40 * 9 = 360. Then, t = 360 / 12 = 30 minutes.

Front

What is the relationship between pressure and volume in an inverse variation problem?

Back

In an inverse variation problem, as pressure increases, volume decreases, and vice versa, typically expressed as V = k/p.