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.
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?
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.