# DETERMINE IF THE RELATIONSHIP IS PROPORTIONAL 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.

## Solutions

Problem 1 :

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

Solution :

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.

Problem 2 :

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

Solution :

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.

Problem 3 :

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

Solution :

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.

Problem 4 :

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

Solution :

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.

Problem 5 :

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

Solution :

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.

Problem 6 :

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

Solution :

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.

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