Direct, Inverse, Combined, Joint Variation

Which of the following represents direct variation?

• y = kx

• y = k/x

• y = x/k

• y = mx + b

Which of the following is NOT a direct variation?

• y = -2x

• y = 1/2x

• 2x + 3y = 2

• 3y = 4x

Write the given statement in a mathematical equation.

r varies jointly as s and w

• r = ksw

• w = ksr

Solve for the constant of variation, k.

y varies jointly as x and z.   x = -2 when y = 24 and z = -4

z varies jointly with x and y. If x = 5, y = -1, and z = 10. Find z when x = -1 and y = 7.

• 14

• 7

• -21

• -7

If y varies jointly with the product of x and z, and y = 1000 when x = 10 and z = 20, find y when x = 8 and z = 10.

• 100

• 300

• 200

• 400

Write the mathematical equation of the given statement: (no spacing, use / for fraction bar) The time (t) needed to answer a set of problems is directly proportional to the number (N) of problems, and inversely proportional to the number of students (P) working on the solutions.

If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.

• 4

• 5

• 8

• 10

If m varies directly as p, and m = 35 when p = 5, find m when p is 6.

• 42

• 36

• 25

• 49

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 5 cm on a side is 250 g, find the weight of the liquid in a cubical container 3 cm on a side.

• 12 g

• 6 g

• 27 g

• 54 g