Lesson Plan: Introduction to Linear Equations

Lesson Objectives

  • Define linear equations
  • Identify components of linear equations
  • Represent linear equations using tables, graphs, and equations
  • Understand concepts of slope and y-intercept

TEKS Standards

  • 7.7A: Represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b.
  • 8.4B: Graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship.
  • 8.4C: Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.
  • 8.5A: Represent linear proportional situations with tables, graphs, and equations in the form of y = kx.
  • 8.5B: Represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0.
  • 8.5I: Write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.

Prerequisite Skills

  • Understanding of variables and algebraic expressions
  • Familiarity with the Cartesian coordinate plane
  • Basic arithmetic operations (addition, subtraction, multiplication, division)

Key Vocabulary

  • Linear equation
  • Variable
  • Coefficient
  • Constant
  • Slope
  • y-intercept

Warm-up Activity (5 minutes)

Introduce the concept of linear equations by showing real-life examples. Use this slide show:

https://www.media4math.com/library/slideshow/applications-linear-equations

This shows these applications of linear equations:

  • Cricket chirps vs. Temperature
  • The cost vs. time for renting equipment
  • Distance vs. time

Then show this slide show to compare and contrast linear and non-linear graphs:

https://www.media4math.com/library/slideshow/linear-vs-non-linear-graphs

Teach (20 minutes)

Definition and Components of Linear Equations

Define linear equations as equations that form a straight line when graphed. Use this slide show that provides video definitions of linear equations and linear functions:

https://www.media4math.com/library/slideshow/linear-equations-and-functions-definitions

Explain the components: variables, coefficients, and constants.

Here are some additional definitions to review:

Identifying Linear Equations

Introduce linear equations in standard form and show how this form relates to the slope-intercept form. Use this slide show:

https://www.media4math.com/library/slideshow/linear-equations-standard-and-slope-intercept-form

Representing Linear Equations

  • Introduce the three ways to represent linear equations: tables, graphs, and algebraic expressions. Use this slide show of examples of multiple representations of linear equations:

https://www.media4math.com/library/slideshow/multiple-representations-linear-equations

  • Demonstrate how to create a table of values and plot points on the coordinate plane. Use this Desmos activity to explore the three representations of linear equations:

https://www.desmos.com/calculator/tfoy9bwov2

  • Explain the concept of slope and y-intercept, and their relationship to the equation's form. Use this Desmos activity to explore slope-intercept form:

https://www.media4math.com/library/40088/asset-preview

Review (10 minutes)

Use this slide show to review linear equations and functions, along with an application of slope:

https://www.media4math.com/library/slideshow/linear-equation-review

You can also assign this worksheet, which reviews multiple representations of linear equations and functions:

https://www.media4math.com/library/34317/asset-preview

Assess (5 minutes)

Administer a 10-question quiz to assess students' understanding of linear equations. The quiz should include questions on identifying linear equations, finding components, and representing them in different forms. 

Quiz

  1. Which of the following is a linear equation?
    a) y = x^2 + 3
    b) 2x + 5y = 10
    c) x^3 - y = 0
    d) 3x - 2y + 4 = 0

     
  2. Identify the coefficient of x in the equation: 4x + 2y = 8.

     
  3. What is the y-intercept of the equation y = 2x + 3?

     
  4. What is the general form of a linear equation in slope-intercept form?

     
  5. What is the general form of a linear equation in standard form?

     
  6. Determine if the equation 5x + 2y - 3 = 0 is linear or non-linear.

     
  7. Which equation represents this situation: The cost of renting a car is \$25 plus $0.20 per mile.
    a) y = 0.2x + 25
    b) y = 25x + 0.2

     
  8. Identify the variables, coefficients, and constant in the equation: y = -2x + 5.

     
  9. Find the slope of the line represented by the equation y = 1/2x + 3.

     
  10. Determine if the equation x^2 + y^2 = 25 is a linear equation or not.

     

Answer Key

  1. b and d
  2. 4
  3. 3
  4. y = mx + b
  5. Ax + By = C
  6. Linear
  7. a
  8. Variables: x, y; coefficients: 1, -2; constant: 5
  9. 1/2
  10. Not a linear equation

 

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