Graphing Relationships: Interpreting Linear Functions

Algebra 1 Grades High School 2:23 Video
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Lesson Description

Learn to analyze and interpret graphs of linear functions, including identifying slope, intercepts, and increasing/decreasing intervals. This lesson focuses on understanding the relationship between variables and their graphical representation.

Video Resource

Interpreting a graph exercise example | Linear equations and functions | 8th grade | Khan Academy

Khan Academy

Duration: 2:23
Watch on YouTube

Key Concepts

  • Slope of a line
  • Intercepts of a line
  • Increasing and decreasing intervals of a function
  • Relationship between x and y values on a graph

Learning Objectives

  • Students will be able to determine the slope of a linear function from its graph.
  • Students will be able to identify intervals where a function is increasing or decreasing.
  • Students will be able to interpret the relationship between x and y values based on a graph.
  • Students will be able to connect the slope and intercepts to the behavior of the function

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a function and how it's represented graphically. Briefly discuss the x and y axes and what they represent in the context of a function.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Interpreting a graph exercise example | Linear equations and functions | 8th grade | Khan Academy'. Instruct students to take notes on key concepts such as slope and intercepts.
  • Guided Practice (15 mins)
    Work through example problems similar to the ones in the video. Focus on identifying the slope from the graph (rise over run) and determining where the function is increasing or decreasing. Emphasize the connection between the graphical representation and the numerical values.
  • Independent Practice (15 mins)
    Assign practice problems where students interpret graphs of linear functions. Provide a worksheet with graphs and questions about slope, intercepts, and increasing/decreasing intervals.
  • Wrap Up (5 mins)
    Review the key concepts and answer any remaining questions. Discuss the importance of understanding graphical representations of functions.

Interactive Exercises

  • Graph Matching
    Provide students with equations of linear functions and have them match the equations to their corresponding graphs. This can be done as a group activity or individually.
  • Slope Scavenger Hunt
    Provide a set of graphs scattered around the room. Students find the graphs and calculate the slope. This encourages movement and active learning.

Discussion Questions

  • How does the slope of a line affect its direction on the graph?
  • What does it mean for a function to be increasing or decreasing?
  • How can you determine the y-intercept of a function from its graph?
  • What does the x-intercept tell us about the function?

Skills Developed

  • Interpreting graphs
  • Calculating slope
  • Analyzing function behavior
  • Problem-solving

Multiple Choice Questions

Question 1:

What does the slope of a line on a graph represent?

Correct Answer: The steepness and direction of the line

Question 2:

If a line is decreasing from left to right, what is the sign of its slope?

Correct Answer: Zero

Question 3:

What is the y-intercept of a graph?

Correct Answer: The point where the line crosses the y-axis

Question 4:

What does it mean for a function to be increasing?

Correct Answer: As x increases, y increases

Question 5:

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 6:

What is the x-intercept of a graph?

Correct Answer: The point where the line crosses the x-axis

Question 7:

Which of the following slopes represents a horizontal line?

Correct Answer: Zero

Question 8:

A line passes through the points (0,3) and (1,5). What is the slope?

Correct Answer: 2

Question 9:

If a line has a y-intercept of -2, where does it cross the y-axis?

Correct Answer: (0, -2)

Question 10:

What type of line has an undefined slope?

Correct Answer: Vertical

Fill in the Blank Questions

Question 1:

The slope of a line is defined as the change in ___ divided by the change in x.

Correct Answer: y

Question 2:

A line that is going uphill from left to right has a ___________ slope.

Correct Answer: positive

Question 3:

The point where a line crosses the y-axis is called the ____-intercept.

Correct Answer: y

Question 4:

If a line is horizontal, its slope is ___________.

Correct Answer: zero

Question 5:

When a function is __________ , the y-values increase as the x-values increase.

Correct Answer: increasing

Question 6:

The point where a line crosses the x-axis is called the ____-intercept.

Correct Answer: x

Question 7:

A line that is going downhill from left to right has a ___________ slope.

Correct Answer: negative

Question 8:

A ________ line has an undefined slope.

Correct Answer: vertical

Question 9:

The slope is a measure of a line's ___________.

Correct Answer: steepness

Question 10:

If the slope of a line is zero, the line is said to be ___________.

Correct Answer: horizontal

Educational Standards

A1.F.1:Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problems. A1.F.3:Represent functions in multiple ways and use the representation to interpret real-world and mathematical problems. 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.

Teaching Materials

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