Name: Date: Period Equations of Proportional Relationships Points to Remember: Proportional relationships have a constant ratio, or unit rate. The constant ratio, or unit rate of y, can also be called the constant of x proportionality. x is known as the independent variable, y is known as the dependent variable Model a Proportional Relationship with an Equation Example 1: John works at an ice cream shop. The hours worked and wages earned are given in the table. Time (x) John s Wages Dollars (y) 2 18 3 27 4 36 a. Find the constant of proportionality and explain what it represents in this situation. b. Write an equation in the form y = kx that will relate the dollars earned to the number of hours worked. c. Use your equation from part (b) to find the amount of dollars John would earn after working 12 hours.
Example 2: Your mother keeps a log where she records the mileage and the number of gallons purchased each time she fills up the tank. The table below shows how many miles she was able to drive on each number of gallons. Gas (x) Mom s Record Miles (y) 8 224 10 280 4 112 a. Find the constant of proportionality and explain what it represents in this situation. b. Write an equation in the form y = kx that will relate the miles driven to the number of gallons of gas. c. Using the equation found in part (b), determine how far your mother can travel on 18 gallons of gas. d. Using the equation found in part (b), determine how many gallons of gas would be needed to travel 750 miles.
Example 3: In 25 minutes, Li can run 10 laps around the track. a. Determine the number of laps she can run per minute. b. Create a table to determine how many laps Li can run in 5, 10, 15, and 20 minutes. Li s Laps Minutes (x) Laps (y) 5 10 15 20 25 10 c. Find the constant of proportionality, or unit rate, in this situation. d. Write an equation in the form y = kx to represent the relationship between time and laps. e. Use the equation from part (d) to determine how many laps Li can run in 60 minutes. f. Use the equation from part (d) to determine how many minutes it would take for Li to run 40 laps.
Name: Date: Equations of Proportional Relationships 1. Allison s middle school team has designed t-shirts containing their team name and color. Print-o-Rama charges a fixed amount for each shirt ordered. The total cost is shown below for the given number of shirts. Print-o-Rama Shirts (x) Cost (y) 0 0 10 80 20 160 50 400 a. What is the constant of proportionality of Print-o-Rama? What does it represent? b. Write an equation relating cost and shirts for Print-o-Rama. 2. On average, Susan downloads 60 songs per month. An online music vendor sells package prices for songs that can be downloaded onto personal digital devices. Susan wants to know if she should buy her music from this company or pay a flat fee of $58 per month offered by another company. Online Music Vendor Number of Songs Purchased (x) Cost (y) 40 36 20 18 12 10.80 5 4.50 a. Find the constant of proportionality for this situation. c. Use your equation to find the cost of 60 songs. Which is the better deal, the online music vendor shown in the table or the flat fee of $58 per month? Explain. Name: Date: Period
Equations of Proportional Relationships Review: How do you find the constant of proportionality? o Divide to find the unit rate, y x How do you write an equation for a proportional relationship? o y = kx, substituting the value of the constant of proportionality in place of k 1. Jennifer is shopping with her mother. They pay $2 per pound for tomatoes at the vegetable stand. a. Find the constant of proportionality in this situation. c. Use the equation to find the price for 3.5 pounds of tomatoes. 2. It cost $15 to send 3 packages through a certain shipping company. Consider the number of packages per dollar. a. Find the constant of proportionality for this situation. c. Use the equation to find the cost to send 7 packages.