Direct and Inverse 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 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 xy = k, where k is a non-zero constant.

Front

If y varies directly with x, and y = 10 when x = 2, what is the value of y when x = 5?

Back

y = 25 (since k = 5 when y = 10 and x = 2, then y = kx = 5*5 = 25).

Front

If x varies inversely with y, and x = 4 when y = 3, what is the value of x when y = 6?

Back

x = 2 (since k = xy = 12 when x = 4 and y = 3, then x = k/y = 12/6 = 2).

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

What is the formula for Inverse Variation?

Back

The formula for Inverse Variation is xy = k, where k is the constant of variation.

Front

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

Back

Two quantities are in direct variation if their ratio is constant.

Front

How do you determine if two quantities are in inverse variation?

Back

Two quantities are in inverse variation if their product is constant.

Front

If the cost of 5 apples is $10, what is the cost of 8 apples assuming direct variation?

Back

The cost of 8 apples is $16 (since the cost per apple is $2, so 8 apples cost 8*2 = $16).

Front

If the speed of a car is 60 mph and the time taken is 2 hours, what is the distance traveled?

Back

The distance traveled is 120 miles (using the formula distance = speed × time).