A.2D 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

What is the equation of direct variation?

Back

The equation of direct variation can be written in the form y = kx, where k is the constant of variation.

Front

If y varies directly as x and y = 6 when x = 2, what is the constant of variation (k)?

Back

k = 3, because y = kx implies 6 = k(2) => k = 6/2 = 3.

Front

If the cost of mailing a package is directly proportional to its weight, what does this imply?

Back

This implies that as the weight of the package increases, the cost to mail it also increases at a constant rate.

Front

Write the direct variation equation for the cost of mailing a package if it costs $8.75 to mail a 5lb package.

Back

The equation is y = 1.75x, where y is the cost and x is the weight in pounds.

Front

Find the cost of mailing a 12lb package using the equation y = 1.75x.

Back

The cost is $21.00, calculated as y = 1.75(12) = 21.

Front

If y = 3/2 when x = 9, what is the direct variation equation?

Back

The equation is y = (1/6)x.

Front

What is the value of y when x = 66 in the equation y = (1/6)x?

Back

y = 11, calculated as y = (1/6)(66) = 11.

Front

A recipe for 3 dozen cookies calls for 4 cups of flour. Write the direct variation equation for the number of cookies (c) and cups of flour (f).

Back

The equation is c = 12f, where c is the number of cookies and f is the cups of flour.

Front

How many cups of flour are needed for 9 dozen cookies?

Back

12 cups, calculated as f = 9/12 = 0.75, so 9 dozen cookies require 12 cups of flour.