Unlocking Proportional Relationships: Writing Equations

Algebra 1 Grades High School 2:47 Video
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Lesson Description

Learn how to identify and write equations for proportional relationships using a real-world example: ice cream scoops and prices!

Video Resource

Writing an equation for a proportional relationship (example) | 7th grade | Khan Academy

Khan Academy

Duration: 2:47
Watch on YouTube

Key Concepts

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

Learning Objectives

  • Identify proportional relationships from a table of values.
  • Determine the constant of proportionality.
  • Write an equation representing a proportional relationship in the form y = kx.
  • Apply proportional relationships to solve real-world problems.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a proportional relationship. Ask students for examples of proportional relationships they might encounter in everyday life (e.g., hours worked and money earned, gallons of gas and distance traveled). Briefly discuss how these relationships can be represented as equations.
  • Video Viewing (7 mins)
    Play the Khan Academy video "Writing an equation for a proportional relationship (example) | 7th grade | Khan Academy". Instruct students to pay attention to how the presenter identifies the proportional relationship and derives the equation. Encourage students to take notes on key steps and vocabulary.
  • Guided Practice (10 mins)
    After the video, work through the example problem together as a class. Ask guiding questions such as: * "How can we determine if the relationship between the number of scoops and the price is proportional?" * "What does the constant of proportionality represent in this context?" * "How can we use the constant of proportionality to write the equation?" Emphasize converting fractions to improper fractions to simplify calculations.
  • Independent Practice (10 mins)
    Provide students with additional practice problems involving proportional relationships. These problems should present data in tables, and students should be able to identify the proportional relationship and write the corresponding equation. Example: A lemonade stand sells lemonade for $2 per cup. Write an equation relating the number of cups sold (x) to the total earnings (y).
  • Wrap-up and Discussion (3 mins)
    Reiterate the key concepts of proportional relationships and equation writing. Address any remaining questions or misconceptions. Assign a similar problem for homework.

Interactive Exercises

  • Table Challenge
    Present students with several tables of data. Some tables should represent proportional relationships, and others should not. Students must identify the proportional relationships and write the corresponding equations for those that are proportional.
  • Graphing Proportionality
    Give students an equation of a proportional relationship (e.g., y = 3x). Have them create a table of values and then graph the relationship on a coordinate plane. Discuss the characteristics of the graph (e.g., it's a straight line passing through the origin).

Discussion Questions

  • What are some real-world examples of proportional relationships?
  • How can you tell if a relationship is proportional from a table of values?
  • What does the constant of proportionality represent in the equation y = kx?

Skills Developed

  • Identifying Proportional Relationships
  • Writing Linear Equations
  • Problem-Solving
  • Data Analysis

Multiple Choice Questions

Question 1:

Which of the following equations represents a proportional relationship?

Correct Answer: y = 3x

Question 2:

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

Correct Answer: The slope

Question 3:

If y = 5x, and x = 4, what is the value of y?

Correct Answer: 20

Question 4:

Which of the following tables represents a proportional relationship?

Correct Answer: x: 1, 2, 3; y: 2, 4, 6

Question 5:

If 2 apples cost $1, what is the constant of proportionality (k) when relating cost (y) to the number of apples (x)?

Correct Answer: 0.5

Question 6:

A graph of a proportional relationship:

Correct Answer: Is a straight line that passes through the origin.

Question 7:

What is the constant of proportionality for the equation y = (3/4)x?

Correct Answer: 3/4

Question 8:

If y is proportional to x, and y = 10 when x = 2, what is the value of k?

Correct Answer: 5

Question 9:

Which equation does NOT represent a proportional relationship?

Correct Answer: y = x + 2

Question 10:

In a proportional relationship, when x doubles, what happens to y?

Correct Answer: y doubles

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 ____.

Correct Answer: slope

Question 3:

If y = 4x, then y is said to be _______ proportional to x.

Correct Answer: directly

Question 4:

In a proportional relationship, the ratio of y to x is always ____.

Correct Answer: constant

Question 5:

If y = kx and k = 7, then for every increase of 1 in x, y increases by ____.

Correct Answer: 7

Question 6:

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

Correct Answer: origin

Question 7:

In the ice cream cone example, the number of scoops is the ______ variable.

Correct Answer: independent

Question 8:

In the ice cream cone example, the price of the cone is the ______ variable.

Correct Answer: dependent

Question 9:

If y/x = 9, then y = ______.

Correct Answer: 9x

Question 10:

The constant of proportionality can be found by dividing any y-value by its corresponding _______.

Correct Answer: x-value

Educational Standards

A1.A.4:Analyze real-world and mathematical problems involving linear equations. A1.A.4.3:Write the equation of the line given its slope and y-intercept, slope and one point, two points, x- and y-intercepts, or a set of data points. A1.F.1:Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problems.

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