Direct and Inverse Variation

Direct Variation

100

Which one is an example of direct Variation: 

y = 5x OR -3x + 2y =0 

 First, Second, Both, or Neither

Both

200

Find the missing variable of Direct Variation 

 (2,y) and (10,15)

y= 3

300

Find the missing variable of Direct Variation 

 (2, 14) and (x, 42)

x=6

400

Does the data in this table represent that y varies directly with x? If it does write an equation. 

 x: 4, 5, 11 

 y: 3, 4.5, 13.5

Is not Direct Variation.

500

The amount of simple interest earned in a savings account varies directly with the amount of money in the savings account. You have $1000 in your savings account and earn $30 in simple interest. How much interest would you earn if you had $1200 in your savings account.

You would earn $36 in simple interest.

Inverse Variation

100

If y varies inversely with x, write and equation. 

 x=9 and y=4

y=36/x

200

The cost of a $100 wedding gift is being split between multiple people. Create a table when x: 3, 4, 5.

y: 33.33, 25, 20

300

Find the missing variable in this inverse variation (4,30) and (3, y)

y=40

400

Select 3 points that will create and inverse variation relation. 

(4,12) (2,24) (6,7) (-2,15) (6, -5) (3, 5) (-16,-3)

(4,12) (2, 24) (-16, -3)

500

Find the missing variable in this inverse variation. (12.4,6.6) and (f,8.8)

f= 9.3

Solve for the Constant

100

Find the Constant and label direct, indirect, or neither: 

x: 2, 7, 10 

y: 35, 10, 7

K=70

Direct

200

Find the Constant and label direct/indirect or neither: 

x: 1.2, 1.5, 2.4 

y: 5, 4, 2.5

K=6

Indirect

300

Find the Constant and label direct/indirect or neither:  x: 2, 6, 10 

y: 4.2, 12.6, 21

k=2.1

Direct

400

Find the Constant and label direct/indirect or neither:  x: 2, 8, 16 

y: 9, 36, 72

k=4.5

Direct

500

Find the Constant and label direct/indirect or neither:  x: 0, 2, 4, 6 

y: 3, 5, 7, 9

There is no constant. 

Neither. 

Word Problems

100

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?

= 60 amps

200

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?

=160 cm^3

300

The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person with a mass of 50 kg?

=33.333 kg of water

400

Your score on a quiz varies directly with how many questions you answer correctly. If you got a 90 on your quiz and you got 30 questions right, what is your constant?

k=3

500

The number of hours it takes for a block of ice to melt varies inversely as the temperature. If it takes 4 hours for a square inch of ice to melt at 60 degrees, find the constant of variation. 

k=240

Graphing

100

Draw an example of a direct variation graph. 

Must be through (0,0)

200

Draw an example of a inverse variation graph. 

Hyperbola's in opposite quadrants

300

Point A (1,4) lies on a line that represents a direct variation equation. Plot three other points on that line. 

(0,0) (8,2) (-1, -4) (-2, -8)

400

Sketch a inverse variation graph with a constant of 20. 

In quadrants 1 and 3. 

500

Sketch a direct variation graph with a constant of -1/2.

Crosses through (0,0) and has a slope of -1/2.