**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 : **

**Problem 5 : **

**Problem 6 : **

**Problem 1 :**

**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 :**

**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 :**

**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 :**

**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 :**

**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 :**

**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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