Direct Variation

Front

What is Direct Variation?

Back

A relationship between two variables where one variable is a constant multiple of the other. If y varies directly with x, then y = kx, where k is the constant of variation.

Front

What is the Constant of Proportionality?

Back

The constant factor (k) that relates two variables in a direct variation. It is the ratio of y to x.

Front

If y varies directly with x and k = 5, what is y when x = 10?

Back

y = 5 * 10 = 50.

Front

How can you determine if a table represents direct variation?

Back

Check if the ratio of y to x is constant for all pairs of values.

Front

If a car travels 60 miles in 1 hour, how far will it travel in 3 hours?

Back

180 miles (60 miles/hour * 3 hours).

Front

What does it mean if a relationship is not a direct variation?

Back

It means that the ratio of y to x is not constant; the relationship does not follow the form y = kx.

Front

If y = 3x, what is the constant of variation?

Back

The constant of variation is 3.

Front

If a recipe requires 2 cups of flour for 4 servings, how much flour is needed for 10 servings?

Back

5 cups (2 cups/4 servings = 0.5 cups/serving; 0.5 cups * 10 servings = 5 cups).

Front

What is the formula for direct variation?

Back

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

Front

If a person earns $15 per hour, how much will they earn in 8 hours?

Back

$120 (15 * 8 = 120).