Graphing Proportional Relationships: Decoding the Line

Algebra 1 Grades High School 3:09 Video
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Lesson Description

Learn how to graph proportional relationships and interpret their key features like slope and unit rate. This lesson uses a Khan Academy video to solidify understanding and problem-solving skills.

Video Resource

Graphing proportional relationships example 3 | 8th grade | Khan Academy

Khan Academy

Duration: 3:09
Watch on YouTube

Key Concepts

  • Proportional relationships
  • Slope as a rate of change
  • Graphing linear equations
  • Unit Rate

Learning Objectives

  • Students will be able to graph a proportional relationship given its equation.
  • Students will be able to identify the slope of a line from its graph or equation.
  • Students will be able to determine if a relationship is proportional based on its equation or graph.
  • Students will be able to connect the unit rate to the slope of the graph.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a proportional relationship (y = kx, where k is the constant of proportionality). Briefly discuss how these relationships appear as straight lines passing through the origin on a graph.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Graphing proportional relationships example 3 | 8th grade | Khan Academy'. Encourage students to take notes on the key steps demonstrated in the video, especially how to find two points on the line and how to interpret the slope.
  • Guided Practice (15 mins)
    Work through an example problem similar to the one in the video, guiding students through the process of finding two points that satisfy the equation, graphing the line, and identifying the slope. Emphasize the connection between the slope and the unit rate of change.
  • Independent Practice (15 mins)
    Provide students with several equations of proportional relationships. Have them graph each relationship, identify the slope, and explain what the slope represents in terms of the relationship.
  • Review and Assessment (5 mins)
    Review the key concepts of the lesson. Administer the multiple-choice and fill-in-the-blank quizzes to assess student understanding.

Interactive Exercises

  • Graphing Activity
    Use an online graphing tool (e.g., Desmos) to allow students to graph proportional relationships and explore how changing the equation affects the graph. Have them manipulate the slope (k) and observe the changes in the line.
  • Real-World Proportions
    Present a scenario that describes a proportional relationship (e.g., earning $15 per hour). Ask students to write the equation, graph the relationship, and explain the meaning of the slope in the context of the scenario.

Discussion Questions

  • How can you tell if a graph represents a proportional relationship?
  • What does the slope of a line tell you about the relationship between the variables?
  • How is the unit rate related to the slope in a proportional relationship?

Skills Developed

  • Graphing linear equations
  • Interpreting slope
  • Identifying proportional relationships
  • Applying mathematical concepts to real-world problems

Multiple Choice Questions

Question 1:

Which of the following equations represents a proportional relationship?

Correct Answer: y = 3x

Question 2:

What is the slope of the line represented by the equation y = 4x?

Correct Answer: 4

Question 3:

A line representing a proportional relationship passes through the point (2, 6). What is the constant of proportionality?

Correct Answer: 3

Question 4:

On a graph of a proportional relationship, what point must the line always pass through?

Correct Answer: (0, 0)

Question 5:

If the slope of a line is 2/3, what happens to y when x increases by 3?

Correct Answer: y increases by 2

Question 6:

Which graph represents a proportional relationship?

Correct Answer: A straight line passing through the origin

Question 7:

The equation y = kx represents a proportional relationship. What does 'k' stand for?

Correct Answer: slope

Question 8:

If y = 5x, and x represents hours worked and y represents money earned, what is the unit rate of earning?

Correct Answer: $5 per hour

Question 9:

Which statement is true about the slope of a proportional relationship?

Correct Answer: The slope is constant

Question 10:

What is another name for slope when discussing proportional relationships?

Correct Answer: unit rate

Fill in the Blank Questions

Question 1:

In a proportional relationship, y is equal to a _________ times x.

Correct Answer: constant

Question 2:

The slope of a line represents the _________ of change.

Correct Answer: rate

Question 3:

On a graph, proportional relationships always pass through the __________.

Correct Answer: origin

Question 4:

The equation y = 7x represents a proportional relationship with a constant of _________.

Correct Answer: 7

Question 5:

If the slope of a line is 5, then for every increase of 1 in x, y increases by _________.

Correct Answer: 5

Question 6:

A line representing a non-proportional relationship will not pass through the __________.

Correct Answer: origin

Question 7:

In the equation y=kx, 'k' is also known as the __________ of proportionality.

Correct Answer: constant

Question 8:

If you work 8 hours and earn $120, your __________ is $15 per hour.

Correct Answer: unit rate

Question 9:

A steeper line on a graph indicates a __________ slope.

Correct Answer: larger

Question 10:

The unit rate is the change in y for every one __________ change in x.

Correct Answer: unit

Educational Standards

A1.A.4.1:Analyze, use and apply mathematical models and other data sets (e.g., graphs, equations, two points, a set of data points) to calculate and interpret slope and the x- and y-intercepts of a line. A1.F.1.1:Distinguish between relations and functions. A1.F.3.1:Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations.

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