Algebra 1 Team Decathlon -- Event #8

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

If y varies directly as x, and y = 10 when x = 8, what is the constant of variation (k)?

Back

k = \frac{y}{x} = \frac{10}{8} = 1.25.

Front

If Maria typed 165 words in 3 minutes, how many words would she type in 1 minute?

Back

Maria types 55 words in 1 minute (165 words / 3 minutes).

Front

If y varies directly as x, and y = 50 when x = 40, what is the value of x when y = 10?

Back

x = \frac{y}{k} = \frac{10}{1.25} = 8.

Front

Which of the following represents a direct variation: {(1,12), (2, 6), (3, 4), (4, 3)} or {(4, 2), (6, 3), (8, 4), (10, 5)}?

Back

{(4, 2), (6, 3), (8, 4), (10, 5)} represents a direct variation.

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

If 15 miles is represented by 3 centimeters on a map, how many centimeters represent 135 miles?

Back

27 cm (using the ratio \frac{3 cm}{15 miles} = \frac{x cm}{135 miles}).

Front

What does it mean if two quantities vary directly?

Back

It means that as one quantity increases, the other quantity increases proportionally.

Front

If y = 3x and x = 5, what is the value of y?

Back

y = 3(5) = 15.

Front

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

Back

y = kx = 2(10) = 20.