Graphing Proportional Relationships: A Visual Journey

Algebra 1 Grades High School 1:11 Video
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Lesson Description

Learn how to graph proportional relationships from tables of values and determine the slope of the line. This lesson uses a Khan Academy video to provide a clear, visual explanation.

Video Resource

Graphing proportional relationships example 2 | 8th grade | Khan Academy

Khan Academy

Duration: 1:11
Watch on YouTube

Key Concepts

  • Proportional Relationships
  • Graphing Linear Equations
  • Slope as Change in Y over Change in X

Learning Objectives

  • Students will be able to graph a proportional relationship given a table of values.
  • Students will be able to calculate the slope of a line from its graph.

Educator Instructions

  • Introduction (5 mins)
    Begin by briefly reviewing what a proportional relationship is (y = kx, where k is the constant of proportionality). Discuss how these relationships always pass through the origin (0,0). Remind students of the definition of slope as rise over run or change in y over change in x.
  • Video Viewing (5 mins)
    Play the Khan Academy video 'Graphing proportional relationships example 2 | 8th grade | Khan Academy'. Instruct students to take notes on the example provided.
  • Guided Practice (10 mins)
    Work through the example from the video again, step-by-step. Emphasize how to identify points from the table and plot them on the graph. Clearly show how to calculate the slope using two points on the line.
  • Independent Practice (10 mins)
    Provide students with a new table of values representing a proportional relationship. Have them graph the relationship and calculate the slope. Provide graph paper and rulers.
  • Wrap-up & Discussion (5 mins)
    Review the independent practice problem and address any student questions. Discuss the relationship between the constant of proportionality and the slope of the line in a proportional relationship.

Interactive Exercises

  • Graphing Challenge
    Present students with a series of tables representing proportional relationships with increasing difficulty (e.g., including fractions or decimals). Challenge them to graph the relationships accurately and quickly. They can compete individually or in teams.

Discussion Questions

  • What does it mean for a relationship to be proportional?
  • How does the slope of a line relate to the proportional relationship?
  • Why do we only need two points to graph a line?

Skills Developed

  • Graphing Linear Equations
  • Calculating Slope
  • Interpreting Data from Tables

Multiple Choice Questions

Question 1:

A proportional relationship always passes through which point?

Correct Answer: (0,0)

Question 2:

What is the formula for calculating the slope of a line?

Correct Answer: Change in y / Change in x

Question 3:

If a line has a slope of 2, what does this mean?

Correct Answer: For every 1 unit increase in x, y increases by 2 units.

Question 4:

Given the points (2, 4) and (4, 8) on a line, what is the slope?

Correct Answer: 1/2

Question 5:

Which of the following equations represents a proportional relationship?

Correct Answer: y = 3x

Question 6:

In a table of values, how can you tell if the relationship is proportional?

Correct Answer: The ratio of y to x is constant.

Question 7:

If x increases and y decreases, the slope is:

Correct Answer: Negative

Question 8:

How many points are needed to define a line?

Correct Answer: 2

Question 9:

What is the y-intercept of a proportional relationship?

Correct Answer: Always 0

Question 10:

The change in y is also known as the?

Correct Answer: Rise

Fill in the Blank Questions

Question 1:

A proportional relationship can be written in the form y = ____x, where k is the constant of proportionality.

Correct Answer: k

Question 2:

The slope of a line is defined as the change in y divided by the change in ____.

Correct Answer: x

Question 3:

Lines with a positive slope go ________ as you move from left to right.

Correct Answer: up

Question 4:

If a line is horizontal, its slope is ____.

Correct Answer: 0

Question 5:

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

Correct Answer: 0

Question 6:

The slope can also be defined as rise over ____.

Correct Answer: run

Question 7:

The constant of proportionality is equal to the ____.

Correct Answer: slope

Question 8:

The point (0,0) is also known as the ____.

Correct Answer: origin

Question 9:

When graphing, the horizontal axis is the ____ axis.

Correct Answer: x

Question 10:

When graphing, the vertical axis is the ____ axis.

Correct Answer: y

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.F.1.2:Identify the dependent variable, independent variable, domain and range given a function, equation, or graph. Identify restrictions on the domain and range in mathematical models.

Teaching Materials

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