Digits, Grade 7, Volume 1, Homework Helper

### 7-3: Proportional Relationships and Equations

#### Key Concept

You have used tables and graphs to represent proportional relationships. An equation can also describe a proportional relationship between two variables.

Recall that when there is a proportional relationship between x and y, y is a constant multiple of x. This constant multiple is the constant of proportionality.

Since the value of y depends on the value of x, y is the dependent variable and x is the independent variable.

#### Part 1

Example Understanding Equations Representing Proportional Relationships

Your friend uses the equation y = 8.5x to calculate the total cost y in dollars for x movie tickets.

• a. What is the constant of proportionality shown in the equation?

• b. What does the constant of proportionality represent in this situation?

• c. How much will 13 movie tickets cost?

Solution

• a. table with 2 rows and 1 column , row1 column 1 , y equals 8.5 x , row2 column 1 , 8.5 equals , y over x , end table

The constant of proportionality is \$8.50 per ticket.

• b. The constant of proportionality represents the unit cost, or the price, y, per movie ticket, x.

• c. To find how much 13 movie tickets will cost, substitute 13 for x.

table with 3 rows and 3 columns , column 2 y , column 3 equals 8.5 x , row2 column 1 , cap substitute . 13 for bold x . , column 2 , column 3 equals 8.5 open 13 close , row3 column 1 , cap multiply. , column 2 , column 3 equals , 110.5 , end table

It will cost \$110.50 for 13 movie tickets.

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