Algebra 1 - 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

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

How do you find the value of y when x = 4, given that y varies directly with x and k = 3?

Back

y = kx = 3 * 4 = 12.

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 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 the amount of money earned is directly proportional to the number of hours worked, and $50 is earned in 2 hours, how much is earned in 8 hours?

Back

$200.

Front

What does it mean if a table of values represents direct variation?

Back

It means that the ratio of y to x is constant for all pairs of values.

Front

If y = 15 when x = 3, what is the value of y when x = 5?

Back

y = (15/3) * 5 = 25.

Front

Is the relationship between the number of tickets sold and the total sales amount a direct variation?

Back

Yes, because total sales amount is directly proportional to the number of tickets sold.

Front

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

Back

5 cups (since flour varies directly with servings).