**Proportional and nonproportional situations using a table :**

If there is not a constant rate of change in the data displayed in a table, then the table represents a nonlinear nonproportional relationship.

A linear relationship represented by a table is a proportional relationship when the quotient of each pair of numbers is constant. Otherwise, the linear relationship is nonproportional.

**Example 1 :**

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

**Solution :**

From the table, find the ratio between each value of "y" and its corresponding value of "x".

y/x = 1/5 = 1/5

y/x = 8/40 = 1/5

y/x = 13/65 = 1/5

Hence, the ratio between the values of "y" and and their corresponding values of "x" is constant. Hence, the relationship represented by the table given above is proportional.

**Example 2 :**

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

**Solution :**

From the table, find the ratio between each value of "y" and its corresponding value of "x".

y/x = 30/2 = 15

y/x = 90/8 = 11.25

y/x = 150/14 = 10.71

Hence, the ratio between the values of "y" and and their corresponding values of "x" is not constant. Hence, the relationship represented by the table given above is nonproportional.

**Example 3 :**

The values in the table represent the numbers of U.S. dollars three tourists traded for Mexican pesos. The relationship is linear. Is the relationship proportional or nonproportional ?

**Solution :**

From the table, find the ratio between each value of "Mexican pesos received" and its corresponding value of "U.S. dollars traded".

Let "M" stand for Mexican pesos received and "U" stand for U.S. dollars traded

U/M = 1,690/130 = 13

U/M = 3,315/255 = 13

U/M = 6,565/505 = 13

Hence, the ratio of pesos received to dollars traded is constant at 13 Mexican pesos per U.S. dollar. This is a proportional relationship.

After having gone through the stuff given above, we hope that the students would have understood, how to use tables to identify proportional and nonproportional situations.

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