CONSTANT OF PROPORTIONALITY WORKSHEET

Problem 1 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality.

Problem 2 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality.

Problem 3 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality.

Problem 4 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality.

Problem 5 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality.

Problem 6 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality.

Problem 7 :

y is directly proportional to x. Given that y = 144 and x = 12. Find the value of y when  x = 7.

Problem 8 :

7 men can complete a work in 52 days. In how many days will 13 men finish the same work?

1. Answer :

Let us get the ratio of x and y for all the given values.

4/48 = 1/12

7/84 = 1/12

10/120 = 1/12

When we take ratio of x and y for all the given values, we get equal value for all the ratios.

Therefore the relationship given in the table is proportional.

When we look at the above table when x gets increased, y also gets increased, so it is direct proportion.

Then, we have

y = kx 

Substitute 4 for x and 48 for y.

48 = k(4)

12 = k

So, the constant of proportionality is 12.

2. Answer :

Let us get the ratio of x and y for all the given values.

1/100 = 1/100

3/300 = 1/100

5/550 = 1/110

6/600 = 1/100

When we take ratio of x and y for all the given values, we don't get equal value for all the ratios.

So, the relationship given in the table is not proportional.

3. Answer :

Find the ratio of x and y for all the given values.

2/1 = 2

4/2 = 2

8/4 = 2

10/5 = 2

When we take ratio of x and y for all the given values, we get equal value for all the ratios.

Therefore, the relationship given in the table is proportional.

When we look at the above table when x gets increased, y also gets increased, so it is direct proportion.

Then, we have

y = kx 

Substitute 2 for x and 1 for y.

1 = k(2)

1/2 = k

So, the constant of proportionality is 1/2.

4. Answer :

Find the ratio of x and y for all the given values. 

1/2 = 1/2

2/4 = 1/2

3/6 = 1/2

4/6 = 2/3

When we take ratio of x and y for all the given values, we don't get equal value for all the ratios.

So, the relationship given in the table is not proportional.

5. Answer :

Find the ratio of x and y for all the given values.

1/23 = 1/23

2/36 = 1/18

5/75 = 1/15

When we take ratio of x and y for all the given values, we don't get equal value for all the ratios.

So, the relationship given in the table is not proportional.

6. Answer :

Find the ratio of x and y for all the given values.

2/4 = 1/2

4/8 = 1/2

6/12 = 1/2

8/16 = 1/2

When we take ratio of x and y for all the given values, we get equal value for all the ratios.

Therefore the relationship given in the table is proportional.

When we look at the above table when x gets increased, y also gets increased, so it is direct proportion.

Then, we have

y = kx

Substitute 2 for x and 4 for y.

4 = k(2)

2 = k

So, the constant of proportionality is 2.

7. Answer :

Because y directly proportional to x, we have

y = kx

Using y = 144 and x = 12, we have to find the constant of proportionality.

144 = 12k

12 = k

Therefore y = 12x. 

Substitute 7 for x.

y = 12(7)

y = 84

So, the value of y is 84 when x = 7.

8. Answer :

This is a situation of inverse proportion.

Because, more men -----> less days.

Let x be the no. of men and y be the no. of days.

Because this is inverse proportion, we have

y = k/x

Substitute 7 for x and 52 for y.

52 = k / 7

364 = k

Therefore  y = 364/x.

Substitute 13 for x.

y = 364/13

y = 28

So, 13 men can complete the work in 28 days.

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