# FIND THE CONSTANT OF PROPORTIONALITY FROM A TABLE

If the ratio of one variable to the other is constant, then the two variables have a proportional relationship,

If x and y have a proportional relationship, the constant of proportionality is the ratio of y to x.

In this section, you will learn, how to find the constant of proportionality from a table which contains the values of x and y.

Example 1 :

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.

3 / 30  =  1 / 10

8 / 80  =  10

10 / 100  =  1/ 10

9 / 60  =  1 / 10

7 / 70  =  1 / 10

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 3 for x and 30 for y.

30  =  k(3)

10  =  k

So, the constant of proportionality is 10.

That is, every concrete block weighs 10 kilograms.

Example 2 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. And also, explain what does the constant of proportionality mean ?

Solution :

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

5 / 15  =  1 / 3

10 / 30  =  1 / 3

6 / 18  =  1 / 3

9 / 27  =  1 / 3

2 / 6  =  1 / 3

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 5 for x and 15 for y.

15  =  k(5)

3  =  k

So, the constant of proportionality is 3.

That is, for every can of paint, you could paint 3 bird houses.

Example 3 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. And also, explain what does the constant of proportionality mean ?

Solution :

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

9 / 342  =  1 / 38

7 / 266  =  1 / 38

6 / 228  =  1 / 38

8 / 304  =  1 / 38

3 / 114  =  1 / 38

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 9 for x and 342 for y.

342  =  k(9)

38  =  k

So, the constant of proportionality is 38.

That is, for every vote for Faye there were 38 votes for Victor.

Example 4 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. And also, explain what does the constant of proportionality mean ?

Solution :

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

6 / 1212  =  1 / 202

4 / 808  =  1 / 202

10 / 2020  =  1 / 202

3 / 606  =  1 / 202

8 / 1616  =  1 / 202

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 6 for x and 1212 for y.

1212  =  k(6)

202  =  k

So, the constant of proportionality is 202.

That is, every chocolate bar has 202 calories.

Example 5 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. And also, explain what does the constant of proportionality mean ?

Solution :

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

7 / 14  =  1 / 2

8 / 16  =  1 / 2

6 / 12  =  1 / 2

10 / 20  =  1 / 2

2 / 4  =  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 6 for x and 1212 for y.

1212  =  k(6)

202  =  k

So, the constant of proportionality is 202.

For each piece of chicken it costs 2 dollars.

Example 6 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. And also, explain what does the constant of proportionality mean ?

Solution :

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

16 / 8  =  2

24 / 12  =  2

12 / 6  =  2

20 / 10  =  2

4 / 2  =  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 gets decreased, so it is inverse proportion.

Then, we have

y  =  k / x

Substitute 16 for x and 8 for y.

8  =  k(16)

1 / 2  =  k

So, the constant of proportionality is 1 / 2.

Example 7 :

Examine the given table and determine if the relationship is proportional. If yes, determine the constant of proportionality. And also, explain what does the constant of proportionality mean ?

Solution :

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

2 / 32  =  1 / 16

5 / 80  =  1 / 16

9 / 144  =  1 / 16

7 / 144  =  1 / 16

10 / 160  =  1 /16

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 gets decreased, so it is inverse proportion.

Then, we have

y  =  kx

Substitute 2 for x and 32 for y.

32  =  k(2)

16  =  k

So, the constant of proportionality is 16.

That is, for every box of candy you get 16 pieces.

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