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 (2/3, 2) and (x,6)

x=2

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

xy = 36

200

The cost of a $100 wedding gift is being split between multiple people. Create a table when x: 2, 4, 5

y: 50, 25, 20

300

Find the missing variable in this inverse variation (4,28) and (3, p)

p=37.33

400

Find the missing variable in this inverse variation (3/4,y) and (2/3,18)

y=16

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 in the inverse variation: x: 2, 7, 10 y: 35, 10, 7

K=70

200

Find the constant for the direct variation x: 1.2, 5, 3 y: 6, 25, 15

K=6

300

Determine what type of variation is represented and find the Constant: x: 2, 6, 10 y: 4.2, 12.6, 21

Direct k=2.1

400

Determine the type of variation and find the Constant: x: 2, 1, 6 y: 9, 18, 3

inverse k = 18

500

Determine if this is a direct variation, inverse variation, or neither x: 0, 2, 4, 6 y: 3, 5, 7, 9

neither

Word Problems

100

The amount of gas used varies directly as miles traveled. Write the variation equation used, if you use 6 gallons to travel 147 miles.

y = 2 / 49 x gal miles

200

Write the direct variation equation: the cost of buying tomatoes is $.78 for 1 pound. Then tell me how much it would cost to buy 5 tomatoes.

y = .78x $3.90 to buy 5 tomatoes

300

The amount of time it takes to complete a project varies inversely to the number of people working on it. It takes 10 people 5 hours. How long would it take 2 people?

xy = 50 2 people would take 25 hours

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, write an equation for this relationship and determine your grade if you got 20 questions correct

y = 3x y=grade x=number correct grade = 60

500

The time, T, to travel a fixed distance varies inverselt with the rate, R, of travel. If T=4 hr. and R=20 mi/hr. , find T when R=50 mi/hr.

T= 1.6 hr.

Square Root Equations

100

What is the first step for solving a square root equation?

Isolate the square root!

200

Solve for x if:

√(x+5)=√(2x-3)

x=8

300

Solve for x if:

5√(x)-20=-5

x=9

400

Solve for x if:

10√(x+2)=30

x=7

500

Solve for x if:

√(x-4)-10=5

x=229