Constant of Proportionality

Constant of Proportionality

100

What is K with proper units?

k = 1.2 miles per hour

200

A ferry transports bikes to an island.  What is k? 

Number of bikes (x)         10         12          14            

Number of trips (y)          5            6            7              

k = 0.5

300

Find the constant of proportionality with correct units

k =46 miles per hour

400

Fred passed notes during class throughout the day. Find the constant of proportionality.  

People (x)        8             9               10            11

Notes (y)         18           19              20            21

It is not proportional - there is no COP.

500

Find the constant of proportionality with correct units

60 miles per hour

Direct Variation: Tables

100

The table shows the amount earned by Harry for selling ice cream. If y varies directly with x, find the missing y value in the table below. 

Cups Sold = x              3         5        7         9

Earnings ($)  = y         12        20      y       36

y = 28

200

Logan works at a local taco shop and makes $9 per hour. If Logans pay is varies directly with the number of hours he works, complete the table to represent his situation. (Find the missing y values.) 

**There are TWO answers.**

Time (x)        0           1/2            1            9

Pay (y)      y             y            9            81

When x = 0, y = 0 

When x = 1/2, y= 4.5 

300

Drew paints portraits. If the number of portraits varies directly with the number of hours spent on each painting, find the missing x value in the table.  

Time (in hours) = x             Number of portraits = y

           x                                          5

           2                                          10

           3                                          15

           4                                          20

x = 1

5 portraits per hour

400

Alice bought old/used/cheap comics.  Find the k (CoP with correct units) if the price in dollars varies directly with the number of comic books she purchased.

Number of comics (x)           6           12             18            

Price (dollars)  (y)                2            4            3   

          

k = 1/3

500

Shawty earns $84 for a 7 hour shift at Chick-fil-la.  The amount of money she earns, y, varies directly to the number of hours worked, x. 

Show this proportional relationship by completing the table. 

Time (in hours) = x                Money Earned = y

           0                                          _______

           1/2                                       _______

           5                                          _______

           _______                                  180

Time (in hours) = x                Money Earned = y

           0                                          ___0____

           1/2                                       ___6____

           5                                          ___60____

           ___15____                                180

Direct Variation: Missing Value

100

If y varies directly as x, then when y = 9 then x = 3.

     What is y when x = 12?

y = 36

200

y varies directly as x. Find the values as indicated:

 If y = -18 when x = 9, find y when x = 7

y = -14

300

In the following problem, y varies directly as x, if y = -3 when x = -4. 

Find x when y = 12

x = 16

400

y varies directly as x. Find the values as indicated:

If y = 6 when x = 9, find x when y = 12

x = 18

500

On a graph, y varies directly with x, so that the following coordinate is used... (-12, 8). 

Find the missing y coordinate in the following sequence. 

(-18, y) 

y = 12 OR (-18, 12)

All things proportional

100

Julie brought 5 pounds of cans to a recycling place and was paid $2. Find the unit rate. (cost per pound)

$0.40/pound

200

What is k mean in y=kx?

Constant of Proportionality

300

What is the fraction version of... 

-2.6666666....

-2 ⅔ 

400

What are the two qualifications to tell if a line on a  graph is proportional?

1. Straight Line

2. Passes through the origin 

500

What is a synonym for constant of proportionality? 

Unit Rate or Direct Variation