Graphing Proportionality: Seeing Relationships Visually

Algebra 1 Grades High School 7:18 Video
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Lesson Description

Explore proportional relationships by identifying them on graphs. Learn to recognize straight lines through the origin as visual representations of proportionality.

Video Resource

How to visually identify proportional relationships using graphs | 7th grade | Khan Academy

Khan Academy

Duration: 7:18
Watch on YouTube

Key Concepts

  • Proportional relationships
  • Linear equations
  • Origin
  • Ratio

Learning Objectives

  • Identify proportional relationships from graphs.
  • Determine if a graph represents a proportional relationship based on whether it is a straight line through the origin.
  • Calculate and compare ratios from tables of data to determine proportionality.
  • Express the relationship between x and y in a proportional relationship

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a proportional relationship: a relationship where the ratio between two variables (Y and X) is constant (Y/X = k). Also mention that proportional relationship can be shown as y = kx.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'How to visually identify proportional relationships using graphs | 7th grade | Khan Academy'. Instruct students to take notes on the key characteristics of graphs that represent proportional relationships.
  • Guided Practice (15 mins)
    Work through examples similar to those in the video. Show a table of data and ask if it is a proportional relationship by finding the ratio of y/x. Also, show graphs and ask students to identify whether they represent proportional relationships and to explain why or why not.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing tables and graphs. Have them identify which represent proportional relationships. Also ask them to express the realtionships shown on the graphs as equations in y = kx form. Have them calculate and show the calculations used to find the ratio of y/x on the tables.
  • Review and Closure (5 mins)
    Review the key concepts: proportional relationships are represented by straight lines that pass through the origin. Also recap how to calculate the ratio of y/x and identify the relationships.

Interactive Exercises

  • Graphing Challenge
    Students are given equations and asked to graph them. Then, they must identify which graphs represent proportional relationships. They should also determine what the ratio of y/x is.
  • Table Analysis
    Students are given tables of data and asked to calculate the ratios between x and y values to determine if a proportional relationship exists. They must also graph the data and determine if it matches their original conclusion.

Discussion Questions

  • What are the key characteristics of a graph that represents a proportional relationship?
  • How can you determine if a relationship is proportional from a table of values?
  • If a line is straight but does not pass through the origin, is it a proportional relationship? Why or why not?

Skills Developed

  • Graph interpretation
  • Ratio and proportion analysis
  • Equation recognition

Multiple Choice Questions

Question 1:

Which of the following graphs represents a proportional relationship?

Correct Answer: A straight line passing through the origin.

Question 2:

In a proportional relationship, what is true about the ratio of Y to X?

Correct Answer: It is constant.

Question 3:

Which equation represents a proportional relationship?

Correct Answer: y = 3x

Question 4:

If a graph is a straight line, but doesn't go through the origin, is it a proportional relationship?

Correct Answer: No, it is never proportional.

Question 5:

What point must a graph pass through to be considered a proportional relationship?

Correct Answer: (0, 0)

Question 6:

If the ratio of y/x is different for two points on a graph, then the graph shows what?

Correct Answer: A non-proportional relationship.

Question 7:

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

Correct Answer: Curved Line

Question 8:

A table has the following (x,y) pairs: (1,5), (2,10), and (3,15). What type of relationship is it?

Correct Answer: Proportional

Question 9:

A table has the following (x,y) pairs: (1,2), (2,5), and (3,8). What type of relationship is it?

Correct Answer: Linear

Question 10:

If a graph goes through the origin but is curved, is it proportional?

Correct Answer: No

Fill in the Blank Questions

Question 1:

A proportional relationship is represented by a ________ line that passes through the ________.

Correct Answer: straight

Question 2:

For a relationship to be proportional, the ratio of Y to X must be ________.

Correct Answer: constant

Question 3:

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

Correct Answer: origin

Question 4:

In the equation y = kx, the 'k' represents the ________ of proportionality.

Correct Answer: constant

Question 5:

If a line does not pass through the origin, it is not a ________ relationship.

Correct Answer: proportional

Question 6:

A proportional relationship can be written in the form y = ________, where k is a constant.

Correct Answer: kx

Question 7:

To check if a table represents a proportional relationship, you must calculate the ________ of y/x for each pair of values.

Correct Answer: ratio

Question 8:

If the graph is a straight line through the origin, then y is ________ proportional to x.

Correct Answer: directly

Question 9:

When x = 0 and y = 0, the proportional relationship ________ the origin

Correct Answer: intersects

Question 10:

In y = kx, 'k' is equal to the ______ divided by _______.

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.2.1:Distinguish between linear and nonlinear (including exponential) functions. Understand that linear functions grow by equal intervals (arithmetic) and that exponential functions grow by equal factors over equal intervals (geometric). A1.F.3.1:Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations.

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