**Representing proportional relationships with equations worksheets :**

Worksheet on representing proportional relationships with tables is much useful to the students who would like to practice problems on finding proportional relationships between two quantities.

1. Meghan earns $12 an hour at her part-time job. Show that the relationship between the amount she earned and the number of hours she worked is a proportional relationship. Then write an equation for the relationship.

2. In 1870, the French writer Jules Verne published 20,000 Leagues Under the Sea, one of the most popular science fiction novels ever written. One definition of a league is a unit of measure equaling 3 miles. Show that the relationship between miles and leagues is a proportional relationship. Then write an equation for the relationship.

**Question 1 :**

Meghan earns $12 an hour at her part-time job. Show that the relationship between the amount she earned and the number of hours she worked is a proportional relationship. Then write an equation for the relationship.

**Answer :**

**Step 1 :**

Make a table relating amount earned to number of hours.

**Step 2 :**

For each number of hours, write the relationship of the amount earned and the number of hours as a ratio in simplest form.

Amount earned : Number of hours

12 : 1 = 12 : 1

24 : 2 = 12 : 1

48 : 4 = 12 : 1

96 : 8 = 12 : 1

Since the ratios for the two quantities are all equal to 12:1, the relationship is proportional.

**Step 3 :**

Write an equation.

Let x represent the number of hours and y represent the amount earned.

Use the ratio as the constant of proportionality in the equation y = kx.

The equation is y = 12x/1 or y = 12x.

**Question 2 :**

In 1870, the French writer Jules Verne published 20,000 Leagues Under the Sea, one of the most popular science fiction novels ever written. One definition of a league is a unit of measure equaling 3 miles. Show that the relationship between miles and leagues is a proportional relationship. Then write an equation for the relationship.

**Answer :**

**Step 1 :**

Make a table relating amount earned to number of hours.

**Step 2 :**

For each number of league, write the relationship of the distance in miles and the distance in leagues as a ratio in simplest form.

Distance in miles : Distance in leagues

3 : 1 = 3 : 1

6 : 2 = 3 : 1

18 : 6 = 3 : 1

36 : 12 = 3 : 1

60,000 : 20,000 = 3 : 1

Since the ratios for the two quantities are all equal to 3:1, the relationship is proportional.

**Step 3 :**

Write an equation.

Let x represent the distance in leagues and and y represent the distance in miles.

Use the ratio as the constant of proportionality in the equation y = kx.

The equation is y = 3x/1 or y = 3x.

After having gone through the stuff given above, we hope that the students would have understood "Representing proportional relationships with equations worksheets".

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