# Comparing Linear Functions and Graphs

Examples, videos and solutions to help Grade 8 students compare the properties of two functions represented in different ways (e.g., tables, graphs, equations and written descriptions).

### New York State Common Core Math Grade 8, Module 5, Lesson 7

Lesson 7 Student Outcomes • Students compare the properties of two functions represented in different ways (e.g., tables, graphs, equations and written descriptions). • Students use rate of change to compare functions (e.g., determining which function has a greater rate of change).

Lesson 7 Closing • We know that functions can be expressed as equations, graphs, tables, and using verbal descriptions. No matter which way the function is expressed, we can compare it with another function.
• We know that we can compare two functions using different methods. Some methods are more efficient than others.

Lesson 7 Classwork

Exercises 1–4

1. Alan and Margot drive at a constant speed. They both drive the same route from City A to City B, a distance of 147 miles. Alan begins driving at 1:40 p.m. and arrives at City at 4:15 p.m. Margot’s trip from City A to City B can be described with the equation y = 64x, where y is the distance traveled and x is the time in hours spent traveling. Who gets from City A to City B faster?
2. You have recently begun researching phone billing plans. Phone Company A charges a flat rate of a month. A flat rate means that your bill will be \$75 each month with no additional costs. The billing plan for Phone Company B is a function of the number of texts that you send that month. That is, the total cost of the bill changes each month depending on how many texts you send. The table below represents the inputs and the corresponding outputs that the function assigns. At what number of texts would the bill from each phone plan be the same? At what number of texts is Phone Company A the better choice? At what number of texts is Phone Company B the better choice?
3. A function describes the volume of water in gallons, y, that flows from faucet A for x minutes. The graph below is the graph of this function. Faucet B’s water flow can be described by the equation y = 5/6 x, where y is the volume of water in gallons that flows from the faucet in x minutes. Assume the flow of water from each faucet is constant. Which faucet has a faster flow of water? Each faucet is being used to fill tubs with a volume of 50 gallons. How long will it take each faucet to fill the tub? How do you know? The tub that is filled by faucet A already has 15 gallons in it. If both faucets are turned on at the same time, which faucet will fill its tub faster?
4. Two people, Adam and Bianca, are competing to see who can save the most money in one month. Use the table and the graph below to determine who will save more money at the end of the month. State how much money each person had at the start of the competition.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 