3-4 Constant of Proportionality

3-4 Constant of Proportionality

Constant of Proportionality 

 $y=kx$     Describes the relationship


 $k=\frac{y}{x}$         $k$  is the constant of proportionality

NOTICE THE FORM OF THE EQUATIONS.   
THERE IS NO ADDING OR SUBTRACTING!

Do these equations represent a proportional relationship?   If so, what is k, the constant of proportionality?

1.    $y=2x$  
2.    $y=5x+1$  
3.     $y-2=6x$  
4.    $y=-\frac{1}{2}x$  

Multiple Choice

Does the equation represent a proportional relationship?   If so, represent the constant of proportionality, k.    $y=0.5x-2$  

• Yes;  0.5

• Yes;  -2

• Yes;  2

• No

Multiple Choice

Does the equation represent a proportional relationship?   If so, represent the constant of proportionality, k.    $y=250x$  

• Yes;  250

• Yes;  -250

• Yes;  x

• No

Multiple Choice

Does the equation represent a proportional relationship?   If so, represent the constant of proportionality, k.    $y=x+1$  

• Yes;  1

• Yes;  -1

• Yes;  x

• No

Using a table

x | y

--------

10 | 8

--------

15 | 12

1. Is the relationship proportional?
2. If so, what is the constant of proportionality?
3. Write an equation as y=kx

Open Ended

x | y

-----

5 | 8

-----

10 | 16

1. Is the relationship proportional?
2. If so, what is k, the constant of proportionality?
3. Write an equation, y=kx, to describe the relationship.

Word Problem

The manager of a concession stand estimates that she needs 5 hot dogs for every 8 people who attend a baseball game. If 1,400 people attend the game, how many hotdogs should the manager order?

Multiple Choice

The store estimates that she needs 7 treats for every 3 cats. If 55 cats are expected, approximately how many treats will the store need?

• 129 treats

• 111 treats

• 105 treats

• 98 treats

Word Problem

A half dozen cookies cost $12. What constant of proportionality relates the number of cookies and total cost? Write an equation to represent the relationship.

Multiple Choice

A half dozen carton of eggs costs $3. What constant of proportionality relates the relationship between the number of eggs and the total cost? Write an equation to represent the relationship.

• y=2x

• y=18x

• y=0.5x

• y=0.2x

Word Problem

Meg's car can travel 114 miles on 4 gallons of gas. If she used 6 gallons of gas, how far did she drive?

Multiple Choice

Lisa's car can travel 145 miles on 5 gallons of gas. If she used 8 gallons of gas, how far did she drive?

• 195 miles

• 212 miles

• 232 miles

• 306 miles