Representing Proportional Relationships by Equations

June is buying fruit from Penny to enter a worlds biggest fruit salad competition. To find out how much money she will spend, June will be representing proportional relationships by equations. June needs to identify the 'unit rate' in cost of fruit per kilogram, which can be represented with the variable . The equation that represents a proportional relationship is written like this is the unit rate is the dependent variable which is affected by the independent variable. is the independent variable, which is the one that is being manipulated by the unit rate. It's important to write a ‘let’ statement to define the variables used. In this case, let represent the total cost since that will be affected by the , and let represent the kilograms of fruit, the independent variable. Let's see which fruit June decides to buy first! The blueberries cost three pounds and seventy-five pence per kilogram. The unit rate, , is three point seven five. Remember the equation equals times . The unit rate is then substituted for in the equation. The variables and will remain variables because , which is the cost, will depend on the amount of kilograms that June buys June will need more than just blueberries if she wants to set the worlds biggest fruit salad record! Penny has grown some pineapples in her garden and is selling them for two pounds and thirty-five pence per kilogram. The unit rate of cost per kilogram for the pineapples is two point three five. Again to find the total cost , the unit rate is substituted into to be multiplied by the kilograms . The equation to represent the proportional relationship of kilograms of pineapples to cost would be equals two point three five times . Penny suggests June add in some of her fresh strawberries because they are in season. The strawberries cost four pounds and fifty pence per kilogram. What is the unit rate of the strawberries? The unit rate is four point five. Don't forget, when we are writing an equation we need to define our let statements. The is the independent variable and will represent the kilograms of strawberries. The is the dependent variable and will represent the total cost of strawberries. How will you write the equation that represents this proportional relationship? equals four point five multiplied by . June decides she has room for one additional type of fruit in her salad, but she wants to add something big! The last fruit she will buy is watermelon, which costs ninety pence per kilogram. Pause here and help June represent the cost of watermelons per kilogram, with an equation. The unit rate is nought point nine. Write let statements for the independent and dependent variables, and write the equation! To summarise, one way we can represent a proportional relationship is by writing an equation. First, identify the unit rate. Next, define the dependent and independent variables with let statements and then write your equation! June is wondering what sort of competition there will be for this contest!