Unlocking Proportional Relationships: Mastering y=kx

Algebra 1 Grades High School 5:00 Video
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Lesson Description

Explore proportional relationships and learn to express them using the equation y=kx. Discover the constant of proportionality and its connection to rates of change.

Video Resource

Equations of proportional relationships | 7th grade | Khan Academy

Khan Academy

Duration: 5:00
Watch on YouTube

Key Concepts

  • Proportional relationships
  • Constant of proportionality (k)
  • Equation y=kx
  • Rate of change

Learning Objectives

  • Identify proportional relationships between two variables.
  • Determine the constant of proportionality (k) in a proportional relationship.
  • Write equations in the form y=kx to represent proportional relationships.
  • Interpret the constant of proportionality as a rate of change.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of ratios and proportions. Ask students to provide examples of real-world situations where two quantities are proportional (e.g., ingredients in a recipe, distance traveled at a constant speed).
  • Video Viewing and Guided Notes (15 mins)
    Play the Khan Academy video "Equations of proportional relationships | 7th grade | Khan Academy." Instruct students to take notes on the key concepts, including the definition of a proportional relationship, how to find the constant of proportionality, and how to write the equation y=kx. Pause the video at key points to clarify concepts and answer questions.
  • Example Problems (15 mins)
    Work through several example problems with the class. Start with simple examples using tables and then move to more complex problems involving real-world scenarios. Emphasize the importance of identifying the constant of proportionality and correctly writing the equation y=kx.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing practice problems. Encourage them to work independently and to ask questions if they get stuck.
  • Wrap-up & Assessment (5 mins)
    Conclude the lesson with a brief review of the key concepts. Administer a short quiz to assess student understanding.

Interactive Exercises

  • Proportionality Challenge
    Present students with various tables and graphs. Have them identify which ones represent proportional relationships and write the corresponding equations in the form y=kx.

Discussion Questions

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

Skills Developed

  • Identifying proportional relationships
  • Writing linear equations
  • Problem-solving
  • Interpreting rate of change

Multiple Choice Questions

Question 1:

Which equation represents a proportional relationship?

Correct Answer: y = 3x

Question 2:

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

Correct Answer: The constant of proportionality

Question 3:

If y = 10 when x = 2 in a proportional relationship, what is the value of k?

Correct Answer: 5

Question 4:

Which table shows a proportional relationship between x and y?

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

Question 5:

The distance traveled is proportional to the time spent driving. If you travel 150 miles in 3 hours, what is the constant of proportionality (speed in miles per hour)?

Correct Answer: 50

Question 6:

Which of the following graphs represents a proportional relationship?

Correct Answer: A line that passes through the origin.

Question 7:

What is another name for the 'constant of proportionality'?

Correct Answer: Rate of change

Question 8:

If the equation of a proportional relationship is y = 8x, what is the value of y when x = 5?

Correct Answer: 40

Question 9:

Which of the following represents a proportional relationship in context?

Correct Answer: The number of pages read and the time spent reading at a consistent pace.

Question 10:

For a proportional relationship, if k = 0.5, what does this mean?

Correct Answer: x is twice y

Fill in the Blank Questions

Question 1:

A proportional relationship can be represented by the equation y = ____, where k is the constant of proportionality.

Correct Answer: kx

Question 2:

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

Correct Answer: rate of change

Question 3:

If y/x is always equal to 7, then the constant of proportionality is ____.

Correct Answer: 7

Question 4:

In a proportional relationship, when x is 0, y is always ____.

Correct Answer: 0

Question 5:

If y = 6x, and y = 24, then x = ____.

Correct Answer: 4

Question 6:

The graph of a proportional relationship is a ____ line that passes through the ____.

Correct Answer: straight, origin

Question 7:

In the formula y = kx, 'k' represents the ____ between x and y.

Correct Answer: relationship

Question 8:

For a proportional relationship, if y doubles, then x ____.

Correct Answer: doubles

Question 9:

The equation y = kx represents ____ variation.

Correct Answer: direct

Question 10:

A table of values represents a proportional relationship if the ratio of y to x is always ____.

Correct Answer: constant

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.

Teaching Materials

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