PROPORTIONAL AND NON PROPORTIONAL RELATIONSHIPS WORKSHEET

Problem 1 :

Determine if each of the following equations represents a proportional or nonproportional relationship.

(i)  q = 2p + (1/2)

(ii)  v = (1/10)u

(iii)  t = 15d

(iv)  m = 0.75d - 2

A linear relationship is a proportional relationship when y/x is constant. Otherwise, the linear relationship is nonproportional.

Solution

Problem 2 :

Determine which of the following tables represent proportional relationships.

(i)	(ii)
Solution (iii)  Solution	Solution (iv) Solution

Problem 3 :

Determine which situation is a proportional relationship and which situation is a nonproportional relationship.

Dylan makes $336 for 32 hours of work, and Angela makes $420 for 42 hours of work.

1) How much do Dylan and Angela each make per hour?

2) Is Dylan’s wage for 25 hours proportional to Amber’s wage for 42 hours? Why or why not?

Solution

Problem 4 :

This year, Andrea celebrated her 12th birthday, and her brother Carlos celebrated his 6th birthday. Andrea noted that she was now twice as old as her brother was. Is the relationship between their ages proportional? Support your answer.

Solution

Problem 5 :

Lily is considering buying books on display three different tables. Each table has one of the following signs.

Offer A : Each Book $10

Offer B : Each book 50% off.

Offer C : Each book $8 for club members (one time membership fee : $15).

What will be the total cost if Lily buys 6 books from the table whose sign indicates a nonproportional relationship?

Solution

Problem 6 :

Complete the tables below and then graph each set of data.

Solution

Problem 7 :

Determine if each of the following graphs represents a proportional or nonproportional relationship.

i)  

Solution

ii)  

If it is a linear equation it can be written in the form y = mx + b . If it is also proportional, then b = 0 and it can also be written as y = kx .

Solution

Asnwer Key

1)  i)  non proportional relationship.

ii)   proportional relationship and constant of proportionality is 1/10.

iii)  proportional relationship and constant of proportionality is 15.

iv)  not proportional relationship, because 0.75d is subtracted with 2

2)

i)  proportional relationship.

ii)   proportional relationship.

iii)  non proportional relationship.

iv)  proportional relationship.

3)  1) Dylan will make $10.5 and Angela will make $10.

2)  Working rate of them are not same, it is not proportional.

4)   the relationship between their ages is proportional.

5)  Offer A and B are proportional and offfer C is non proportional.

6)  

7)  i)  the required linear equation is y = x + 1.

ii)  the required equation is y = (1/4)x.

Problem 1 :

Determine if each of the following equations represents a proportional or nonproportional relationship.

(i)  d = 65t

(ii)  p = 0.1s + 2000

(iii)  n = 450 − 3p

(iv)  36 = 12d

A linear relationship is a proportional relationship when y/x is constant. Otherwise, the linear relationship is nonproportional.

Solution

From the Table

Problem 2 :

Determine if the linear relationship represented by each table is a proportional or nonproportional relationship.

(i) When x = 2, y = 30 When x = 8, y = 90 Solution

(ii) Solution

From the Statement

Problem 3 :

Determine which situation is a proportional relationship and which situation is a nonproportional relationship.

(i)  The cost for Test Prep Center A is $20 times the number of hours that you attend. 

(ii)  The cost for Test Prep Center B is $25 an hour, but you have a $100 coupon that you can use to reduce the cost.

Solution

From the Graph

Problem 4 :

Determine if each relationship is a proportional or nonproportional situation.

(i)

ii)  

Solution

Problem 5 :

You swam for 16 minutes and completed 20 laps. You swam your first 4 laps in 2.4 minutes. How long does it take you to swim 10 laps?

Solution

Problem 6 :

Find the heart rates of yourself and your friend. Do these rates form a proportion? Explain.

Solution

Problem 7 :

You earn $56 walking your neighbor’s dog for 8 hours. Your friend earns $36 painting your neighbor’s fence for 4 hours. Are the pay rates equivalent? Explain.

Solution

Problem 8 :

The shadow of the moon during a solar eclipse traveled 2300 miles in 1 hour. In the first 20 minutes, the shadow traveled 766  2/3 miles. How long did it take for the shadow to travel 1150 miles? Justify your answer.

Solution