Direct and Inverse Variation Worksheet



Algebra 2

9.1 D1 Direct, Inverse, & Joint Variation Name:____________________________ P. _____

Write an equation for the given relationship.

1) y varies jointly with m and the square root of b. _________________________

2) y varies inversely with the square of x. _________________________

3) z varies inversely with x and jointly with y and w. _________________________

4) a varies directly with c and inversely with d. _________________________

Classify the following as Direct (D), Inverse (I), Joint (J), or No (No) Variation.

5) m = -5p D I J No 6) c = [pic] D I J No

7) c = 3vm D I J No 8) r = [pic] D I J No

9) n = ½ f D I J No 10) uw = -18 D I J No

Write an equation relating the variables, then find the missing variable:

11) y varies directly with x. If y = –4 when x = 2, find y when x = –6.

Equation: ________________________ y = _________

12) y varies inversely with x. If y = 40 when x = 16, find y when x = –5.

Equation: ________________________ y = _________

13) y is inversely proportional to x. If y = 7.5 when x = 8, find x when y = 5.

Equation: ________________________ x = _________

14) r is directly proportional to the square of x. If r = 72 when x = 12, find r when x = 8.

Equation: ________________________ r = _________

15) z varies jointly with x and y. If x = 12, y = 4, and z = 2, find z when x = 2 and y = 6.

Equation: ________________________ z = _________

16) p varies jointly with q and the cube of r. If p = 270 when q = 6 and r = 3, find p when q = 3 and r = 5.

Equation: ________________________ p = _________

Answer the following questions.

17) If x and y vary directly, as x decreases, what happens to the value of y? ____________________

18) If x and y vary inversely, as y increases, what happens to the value of x? ___________________

19) If x and y vary directly, as y increases, what happens to the value of x? ___________________

Answer the following questions:

20) The electric current I, is amperes, in a circuit varies directly as the voltage V. When 12 volts are applied,

the current is 4 amperes. What is the current when 18 volts are applied?

________________________

21) The volume V of gas varies inversely to the pressure P. The volume of a gas is 200 cm3 under pressure

of 32 kg/cm2. What will be its volume under pressure of 40 kg/cm2?

________________________

22) For Tim’s savings account, the interest earned varies jointly with the principal and the amount of time (in years) since opening the account. If Tim opened the account 3 years ago with $1200 and earned $144 in interest, how much interest will he have earned 8 years after opening the account?

________________________

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