**Find the constant of proportionality from a table :**

Two variables have a proportional relationship if the ratio of one variable to the other is constant.

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

Let us see some example problems based on the above concept.

**Example 1 :**

Determine the constant of proportionality for each table.

**Solution :**

To find the constant of proportionality, we have to divide y by x.

**Ratio of y to x :**

(i) 30/3 = 10

(ii) 80/8 = 10

(iii) 100/10 = 10

(iv) 60/6 = 10

(v) 70/7 = 10

The ratio for each pair of x- and y-values is 10. So, the variables have a proportional relationship.

Every concrete block weighs 10 kilograms.

**Example 2 :**

Determine the constant of proportionality for each table.

**Solution :**

To find the constant of proportionality, we have to divide y by x.

**Ratio of y to x :**

(i) 15/5 = 3

(ii) 30/10 = 3

(iii) 18/6 = 3

(iv) 27/9 = 3

(v) 6/2 = 3

The ratio for each pair of x- and y-values is 3. So, the variables have a proportional relationship.

For every can of paint you could paint 3 bird houses.

**Example 3 :**

**Determine the constant of proportionality for each table.**

**Solution :**

To find the constant of proportionality, we have to divide y by x.

**Ratio of y to x :**

(i) 342/9 = 38

(ii) 266/7 = 38

(iii) 228/6 = 38

(iv) 304/8 = 38

(v) 114/3 = 38

The ratio for each pair of x- and y-values is 38. So, the variables have a proportional relationship.

For Every vote for Faye there were 38 votes for Victor.

**Example 4 :**

**Determine the constant of proportionality for each table.**

**Solution :**

To find the constant of proportionality, we have to divide y by x.

**Ratio of y to x :**

(i) 1212/6 = 202

(ii) 808/4 = 202

(iii) 2020/10 = 202

(iv) 606/3 = 202

(v) 1616/8 = 202

The ratio for each pair of x- and y-values is 202. So, the variables have a proportional relationship.

Every chocolate bar has 202 calories.

**Example 5 :**

**Determine the constant of proportionality for each table.**

**Solution :**

To find the constant of proportionality, we have to divide y by x.

**Ratio of y to x :**

(i) 14/7 = 2

(ii) 16/8 = 2

(iii) 12/6 = 2

(iv) 20/10 = 2

(v) 4/2 = 2

The ratio for each pair of x- and y-values is 2. So, the variables have a proportional relationship.

For each piece of chicken it costs 2 dollars.

**Example 6 :**

**Determine the constant of proportionality for each table.**

**Solution :**

To find the constant of proportionality, we have to divide y by x.

**Ratio of y to x :**

(i) 32/2 = 16

(ii) 80/5 = 16

(iii) 144/9 = 16

(iv) 112/7 = 16

(v) 160/10 = 16

The ratio for each pair of x- and y-values is 16. So, the variables have a proportional relationship.

For every box of candy you get 16 pieces.

After having gone through the stuff given above, we hope that the students would have understood "Find the constant of proportionality from a table".

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