# Lesson Plan: Introduction to Linear Equations

## Lesson Objectives:

- Define linear equations and their components (variables, coefficients, constants)
- Identify linear equations from given equations or word problems
- Represent linear equations using tables, graphs, and algebraic expressions

## Common Core Standards:

- 8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph.
- 8.EE.C.7: Solve linear equations in one variable.

## 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:

- Slope:
__https://www.media4math.com/library/74617/asset-preview__ - y-intercept:
__https://www.media4math.com/library/74608/asset-preview__ - Coefficient:
__https://www.media4math.com/library/74631/asset-preview__

**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**

- 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 - Identify the coefficient of x in the equation: 4x + 2y = 8.
- What is the y-intercept of the equation y = 2x + 3?
- What is the general form of a linear equation in slope-intercept form?
- What is the general form of a linear equation in standard form?
- Determine if the equation 5x + 2y - 3 = 0 is linear or non-linear.
- 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 - Identify the variables, coefficients, and constant in the equation: y = -2x + 5.
- Find the slope of the line represented by the equation y = 1/2x + 3.
- Determine if the equation x^2 + y^2 = 25 is a linear equation or not.

### Answers

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

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