Representing Proportional Relationships by Equations

June is buying fruit from Penny to enter a world's 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 pound, which can be represented with the variable k. The equation that represents a proportional relationship is written like this, k is the unit rate. Y is the dependent variable which is affected by the independent variable. X 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 y represent the total cost since that will be affected by the x, and let x represent the pounds of fruit, the independent variable. Let's see which fruit June decides to buy first! The blueberries cost three dollars and seventy-five cents per pound. The unit rate, k, is three and seventy-five hundredths. Remember the equation y equals k times x. The unit rate is then substituted for k in the equation. The variables y and x will remain variables because y, which is the cost, will will depend on the x amount of pounds 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 dollars and thirty-five cents per pound. The unit rate of cost per pound for the pineapples is two and thirty-five hundredths. Again to find the total cost y, the unit rate is substituted into k to be multiplied by the pounds x. The equation to represent the proportional relationship of pounds of pineapples to cost would be y equals two and thirty-five hundredths times x. Penny suggests June add in some of her fresh strawberries because they are in season. The strawberries cost four dollars and fifty cents per pound. What is the unit rate of the strawberries? The unit rate is four and five tenths. Don't forget when we are writing an equation we need to define our let statements. The x is the independent variable and will represent the pound of strawberries. The y is the dependent variable and will represent the total cost of strawberries. How will you write the equation that represents this proportional relationship? Y equals four and five-tenths multiplied by x. 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 cost ninety cents per pound. Pause here and help June represent the cost of watermelons per pound, with an equation. The unit rate is nine-tenths. Write let statements for the independent and dependent variables, and write the equation! To summarize, 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!