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. It can be expressed as y = kx, where k is a non-zero constant.

Front

How can you identify a direct variation from a table of values?

Back

A table represents direct variation if the ratio of y to x (y/x) is constant for all pairs of values.

Front

If y varies directly with x, what happens to y when x is doubled?

Back

If x is doubled, y will also double, since they are directly proportional.

Front

What is the constant of variation in the equation y = 3x?

Back

The constant of variation is 3.

Front

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

Back

180 miles (since distance varies directly with time).

Front

If y = 5 when x = 1, what is the value of y when x = 4?

Back

y = 20 (since y varies directly with x, y = 5 * 4).

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

Back

5 cups of flour (since the amount of flour varies directly with the number of servings).

Front

Does the following table represent direct variation? (x: 1, y: 2), (x: 2, y: 4), (x: 3, y: 6)

Back

Yes, because the ratio y/x is constant (2).

Front

If a person earns $15 per hour, how much will they earn in 10 hours?

Back

$150 (since earnings vary directly with hours worked).