Decoding Proportionality: Unveiling the Constant from Graphs

Algebra 1 Grades High School 1:50 Video
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Lesson Description

Explore proportional relationships and master the art of identifying the constant of proportionality from graphs. This lesson uses a Khan Academy video to provide a clear, visual understanding of this key algebraic concept.

Video Resource

Constant of proportionality from graph | 7th grade | Khan Academy

Khan Academy

Duration: 1:50
Watch on YouTube

Key Concepts

  • Proportional Relationship
  • Constant of Proportionality
  • Graphical Representation of Proportionality
  • Equation of a Proportional Relationship (y = kx)

Learning Objectives

  • Students will be able to define and identify proportional relationships.
  • Students will be able to determine the constant of proportionality from a graph.
  • Students will be able to express a proportional relationship as an equation (y = kx).
  • Students will be able to create a table of x and y values from a graph and determine the constant of proportionality.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a proportional relationship. Ask students for real-world examples. Introduce the concept of a constant of proportionality and its significance.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Constant of proportionality from graph'. Instruct students to take notes on the method Sal uses to find the constant of proportionality.
  • Guided Practice (10 mins)
    Work through examples similar to the video, guiding students to identify points on the graph, create x-y tables, and determine the constant of proportionality. Emphasize the relationship between the graph and the equation y = kx.
  • Independent Practice (10 mins)
    Provide students with graphs of proportional relationships and have them independently find the constant of proportionality and write the corresponding equations.
  • Wrap-up and Discussion (3 mins)
    Review key concepts and address any remaining questions. Emphasize the importance of proportional relationships in various mathematical contexts.

Interactive Exercises

  • Graphing Challenge
    Provide students with constants of proportionality and have them graph the corresponding proportional relationships on coordinate planes.
  • Constant Detective
    Present students with multiple graphs; they identify which one shows a given constant of proportionality.

Discussion Questions

  • What are some real-world examples of proportional relationships?
  • How can you tell if a graph represents a proportional relationship?
  • How is the constant of proportionality related to the slope of the line?
  • Why does a proportional relationship always pass through the origin (0,0)?

Skills Developed

  • Graph interpretation
  • Algebraic reasoning
  • Problem-solving
  • Equation writing

Multiple Choice Questions

Question 1:

What is the constant of proportionality in the equation y = 5x?

Correct Answer: 5

Question 2:

If a graph shows a proportional relationship, what point must it always pass through?

Correct Answer: (0,0)

Question 3:

On a graph of a proportional relationship, if y = 8 when x = 2, what is the constant of proportionality?

Correct Answer: 4

Question 4:

Which equation represents a proportional relationship?

Correct Answer: y = 3x

Question 5:

If the constant of proportionality is 7, what is the equation of the relationship?

Correct Answer: y = 7x

Question 6:

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

Correct Answer: The constant of proportionality

Question 7:

A graph shows a line that passes through (1, 4). If it is a proportional relationship, what is the constant of proportionality?

Correct Answer: 4

Question 8:

Which of the following is NOT a characteristic of a proportional relationship graph?

Correct Answer: It curves upward

Question 9:

If y varies proportionally with x, and y=10 when x=2, find y when x=5.

Correct Answer: 4

Question 10:

Which point on the graph would help you easily find the constant of proportionality?

Correct Answer: (1,k)

Fill in the Blank Questions

Question 1:

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

Correct Answer: k

Question 2:

The constant of proportionality is the value you _______ x by to get y.

Correct Answer: multiply

Question 3:

A graph of a proportional relationship always passes through the ______.

Correct Answer: origin

Question 4:

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

Correct Answer: slope

Question 5:

If y = 6x, the constant of proportionality is ______.

Correct Answer: 6

Question 6:

If the points (1,5), (2,10), and (3,15) are on a graph, the constant of proportionality is ______.

Correct Answer: 5

Question 7:

In a proportional relationship, as x increases, y _______ proportionally.

Correct Answer: increases

Question 8:

The point (4, 20) lies on a graph of a proportional relationship. The constant of proportionality is ______.

Correct Answer: 5

Question 9:

For a graph showing a proportional relationship if x=3 and y=12 then the constant is ________

Correct Answer: 4

Question 10:

The slope of a proportional relationship always has a y-intercept of ______.

Correct Answer: 0

Educational Standards

A1.A.4:Analyze real-world and mathematical problems involving linear equations. 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.

Teaching Materials

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