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:

  1. A straight line graph that passes through the origin (0, 0).
  2. A constant unit rate (slope).

Observations:

  1. Bob's line: It does not pass through the origin, so it is not proportional.
  2. Renee's line: It passes through the origin and is a straight line, so it represents a proportional relationship.
  3. 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).

  1. Renee's unit rate: From the graph, Renee passes 6 levels in 3 minutes, so the unit rate is 63=2\frac{6}{3} = 2. The ordered pair representing the unit rate is (1,2)(1, 2).
  2. Morgan's unit rate: From the graph, Morgan passes 3 levels in 3 minutes, so the unit rate is 33=1\frac{3}{3} = 1. The ordered pair representing the unit rate is (1,1)(1, 1).

Final Answers:

  • Part A: Renee and Morgan represent proportional relationships.
  • Part B: Ordered pairs: Renee (1,2)(1, 2), Morgan (1,1)(1, 1).

Let me know if you'd like additional details or clarifications!

Expanding Questions:

  1. How is a proportional relationship mathematically defined in general?
  2. Can you find the slope for Bob's line? How does it differ from proportional relationships?
  3. Why is passing through the origin crucial for proportionality?
  4. How can you verify the unit rate from any point on Renee or Morgan's lines?
  5. What real-world situations mirror proportional relationships?

Tip: Always verify proportionality by confirming both the straight line and origin criteria!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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

-

Suitable Grade Level

Grades 6-8