Decoding Proportionality: Interpreting Graphs

Algebra 1 Grades High School 2:42 Video
Print Lesson Plan Watch Video

Lesson Description

Explore graphs of proportional relationships to understand how they represent real-world situations and calculate constants of proportionality.

Video Resource

Interpreting graphs of proportional relationships | 7th grade | Khan Academy

Khan Academy

Duration: 2:42
Watch on YouTube

Key Concepts

  • Proportional Relationships
  • Constant of Proportionality
  • Graphical Representation of Proportionality

Learning Objectives

  • Students will be able to identify proportional relationships from graphs.
  • Students will be able to determine the constant of proportionality from a graph.
  • Students will be able to interpret the meaning of points on a graph of a proportional relationship in a real-world context.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a proportional relationship and its algebraic representation (y = kx). Briefly discuss how proportional relationships are represented graphically as straight lines passing through the origin.
  • Video Viewing and Analysis (10 mins)
    Watch the Khan Academy video 'Interpreting graphs of proportional relationships'. Encourage students to take notes on key concepts and the steps involved in analyzing the graph and determining the constant of proportionality.
  • Guided Practice (15 mins)
    Work through the example from the video, pausing at key points to ask students questions and elicit their understanding. Emphasize the connection between the graph, the equation (y = kx), and the real-world context.
  • Independent Practice (15 mins)
    Provide students with additional graph examples of proportional relationships. Have them identify the constant of proportionality and interpret the meaning of specific points on the graph. You can use the interactive exercises provided below or create similar problems.

Interactive Exercises

  • Graph Matching
    Present students with several graphs and corresponding real-world scenarios. Have them match each graph to the scenario it represents.
  • Constant Calculation
    Provide students with graphs of proportional relationships and have them calculate the constant of proportionality using different points on the graph.

Discussion Questions

  • How can you tell if a graph represents a proportional relationship?
  • What does the constant of proportionality represent in a real-world context?
  • How can you find the constant of proportionality from a graph?

Skills Developed

  • Graph Interpretation
  • Analytical Thinking
  • Problem-Solving
  • Equation Solving

Multiple Choice Questions

Question 1:

Which of the following is true about the graph of a proportional relationship?

Correct Answer: It is a straight line through the origin.

Question 2:

The constant of proportionality in a graph of a proportional relationship represents the:

Correct Answer: slope

Question 3:

In the equation y = kx, what does 'k' represent?

Correct Answer: The constant of proportionality

Question 4:

If a graph shows the cost of bananas versus the number of bananas, and the point (5, $2) is on the graph, what is the cost of one banana?

Correct Answer: $0.40

Question 5:

If the constant of proportionality is 4, which equation represents the proportional relationship?

Correct Answer: y = 4x

Question 6:

A graph represents the distance traveled by a car versus time. If the graph passes through the point (2 hours, 100 miles), what is the car's speed (constant of proportionality)?

Correct Answer: 50 miles/hour

Question 7:

Which of the following equations represents a proportional relationship?

Correct Answer: y = 5x

Question 8:

If a graph of a proportional relationship is steeper, what does that indicate about the constant of proportionality?

Correct Answer: It is larger.

Question 9:

On a graph of a proportional relationship, the y-axis represents the ________ variable.

Correct Answer: dependent

Question 10:

If the point (0,5) lies on a graph, can this represent a proportional relationship?

Correct Answer: No

Fill in the Blank Questions

Question 1:

A proportional relationship can be represented by the equation y = ____.

Correct Answer: kx

Question 2:

The constant of proportionality is also known as the ____ of the line.

Correct Answer: slope

Question 3:

The graph of a proportional relationship always passes through the ____.

Correct Answer: origin

Question 4:

If y = 3x, and x = 5, then y = ____.

Correct Answer: 15

Question 5:

In a proportional relationship, if one variable doubles, the other variable also ____.

Correct Answer: doubles

Question 6:

The ratio between two proportional quantities is always ____.

Correct Answer: constant

Question 7:

A line that rises from left to right has a ____ slope.

Correct Answer: positive

Question 8:

The variable 'x' is also known as the ____ variable.

Correct Answer: independent

Question 9:

If the graph of a proportional relationship is a horizontal line, the constant of proportionality is ____.

Correct Answer: 0

Question 10:

A graph that doesn't pass through the origin can't represent a ____ relationship.

Correct Answer: proportional

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.3.1:Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations. A1.A.4.5:Analyze and interpret associations between graphical representations and written scenarios.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans