• Students examine situations to decide whether two quantities are proportional to each other by checking for a constant multiple between measures of x and measures of y when given in a table or when required to create a table.
• Students study examples of relationships that are not proportional in addition to those that are.
One quantity is proportional to a second if a constant (number) exists such that each measure in the first quantity multiplied by this constant gives the corresponding measure in the second quantity.
Steps to determine if two quantities in a table are proportional to each other:
For each given measure of Quantity A and Quantity B, find the value of B/A
If the value of B/A is the same for each pair of numbers, then the quantities are proportional to each other.
A table of values is proportional if you can multiply the input by a constant number to get the output.
Lesson 3 Examples
For Examples 1–3, determine if y is proportional to x. Justify your answer.
1. The table below represents the amount of snowfall in 5 counties (in inches) to hours of a recent winter storm.
2. The table below shows the relationship between cost of renting a movie to the number of days on rent.
3. The table below shows the relationship between the amount of candy (pounds) bought and the total cost.
4. Randy is planning to drive from New Jersey to Florida. Randy recorded the distance traveled and the total number of gallons used every time he stopped for gas.
Assume miles driven is proportional to Gallons Consumed in order to complete the table.