Library

IM: 8.3.4: Comparing Proportional Relationships (Lesson)

By Newsela Staff
Last updated 2 months ago
13 Questions
4.1: What's the Relationship?
The equation y=4.2x could represent a variety of different situations.
1.

Write a description of a situation represented by this equation. Decide what quantities x and y represent in your situation.

2.

Make a table and a graph that represent the situation.

4.2: Comparing Two Different Representations
Elena babysits her neighbor’s children. Her earnings are given by the equation y=8.40x, where x represents the number of hours she worked and y represents the amount of money she earned.

Jada earns $7 per hour mowing her neighbors’ lawns.
3.

Who makes more money after working 12 hours? How much more do they make? Explain your reasoning by creating a graph or a table.

4.

What is the rate of change for each situation and what does it mean?

5.

Using your graph or table, determine how long it would take each person to earn $150.

Clare and Han have summer jobs stuffing envelopes for two different companies.

Han earns $15 for every 300 ​​​​​envelopes he finishes.

Clare’s earnings can be seen in the table.

6.

By creating a graph, show how much money each person makes after stuffing 1,500 envelopes.

7.

What is the rate of change for each situation and what does it mean?

8.

Using your graph, determine how much more money one person makes relative to the other after stuffing 1,500 envelopes.  Explain or show your reasoning.

Tyler plans to start a lemonade stand and is trying to perfect his recipe for lemonade. He wants to make sure the recipe doesn’t use too much lemonade mix (lemon juice and sugar) but still tastes good.

Lemonade Recipe 1 is given by the equation y=4x where x represents the amount of lemonade mix in cups and y represents the amount of water in cups.

Lemonade Recipe 2 is given in the table.

9.

If Tyler had 16 cups of lemonade mix, how many cups of water would he need for each recipe? Explain your reasoning by creating a graph or a table.

10.

What is the rate of change for each situation and what does it mean?

11.

Tyler has a 5-gallon jug (which holds 80 cups) to use for his lemonade stand and 16 cups of lemonade mix. Which lemonade recipe should he use? Explain or show your reasoning.

Are you ready for more?
Han and Clare are still stuffing envelopes. Han can stuff 20 envelopes in a minute, and Clare can stuff 10 envelopes in a minute. They start working together on a pile of 1,000 envelopes.
12.

How long does it take them to finish the pile?

13.

Who earns more money?