**Write equations for proportional relationships from tables :**

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

A proportional relationship between x and y can be modeled by the equation y = kx.

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

**Example 1 :**

Determine the constant of proportionality for each table and also write an equation for the relationship between *x* and y.

**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.

So,every concrete block weighs 10 kilograms. A proportional relationship between x and y can be modeled by the equation y = kx.

Here the value of k is 10.

Hence the required equation for the relationship between *x* and y is y = 10x.

**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.

So, every can of paint you could paint 3 bird houses.

A proportional relationship between x and y can be modeled by the equation y = kx.

Here the value of k is 3.

Hence the required equation for the relationship between *x* and y is y = 3x.

**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.

So, every vote for Faye there were 38 votes for Victor.

A proportional relationship between x and y can be modeled by the equation y = kx.

Here the value of k is 38.

Hence the required equation for the relationship between *x* and y is y = 38x.

**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.

So,every chocolate bar has 202 calories.

A proportional relationship between x and y can be modeled by the equation y = kx.

Here the value of k is 202.

Hence the required equation for the relationship between *x* and y is y = 202x.

**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.

A proportional relationship between x and y can be modeled by the equation y = kx.

Here the value of k is 2.

Hence the required equation for the relationship between *x* and y is y = 2x.

**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.

A proportional relationship between x and y can be modeled by the equation y = kx.

Here the value of k is 16.

Hence the required equation for the relationship between *x* and y is y = 16x.

After having gone through the stuff given above, we hope that the students would have understood "Write equations for proportional relationships from tables".

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