Math Problem Statement
The graph below shows the total number of levels passed in a video game based on the amount of time, in minutes, they spent playing. Each player is represented by a line on the graph. Part A: Which video game player(s) represents a proportional relationship between the time spent playing the game, in minutes, and the number of levels passed? Provide justification for each of the three graphs. Part B: What is the ordered pair(s) that represents the unit rate based on the graph above?
Solution
Let's analyze this step by step:
Part A:
A proportional relationship is characterized by:
- A straight line graph that passes through the origin (0, 0).
- A constant unit rate (slope).
Observations:
- Bob's line: It does not pass through the origin, so it is not proportional.
- Renee's line: It passes through the origin and is a straight line, so it represents a proportional relationship.
- Morgan's line: It passes through the origin and is a straight line, so it also represents a proportional relationship.
Part B:
The unit rate is the slope of the line, which can be found by calculating the rise (levels passed) over the run (time in minutes).
- Renee's unit rate: From the graph, Renee passes 6 levels in 3 minutes, so the unit rate is . The ordered pair representing the unit rate is .
- Morgan's unit rate: From the graph, Morgan passes 3 levels in 3 minutes, so the unit rate is . The ordered pair representing the unit rate is .
Final Answers:
- Part A: Renee and Morgan represent proportional relationships.
- Part B: Ordered pairs: Renee , Morgan .
Let me know if you'd like additional details or clarifications!
Expanding Questions:
- How is a proportional relationship mathematically defined in general?
- Can you find the slope for Bob's line? How does it differ from proportional relationships?
- Why is passing through the origin crucial for proportionality?
- How can you verify the unit rate from any point on Renee or Morgan's lines?
- What real-world situations mirror proportional relationships?
Tip: Always verify proportionality by confirming both the straight line and origin criteria!
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Math Problem Analysis
Mathematical Concepts
Proportional relationships
Slope of a line
Graph interpretation
Formulas
Slope formula: (rise/run)
Definition of proportional relationship: straight line passing through the origin
Theorems
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Suitable Grade Level
Grades 6-8