Mathematics - Solve and Graph Linear Equations

Objective: 

Students will be able to solve and graph linear equations in two variables.

Materials:

• Whiteboard or blackboard
• Markers or chalk
• Handout or worksheet with practice problems

Introduction (10 minutes):

• Review what a linear equation is and how it can be written in slope-intercept form (y = mx + c).
• Use examples to show how the slope (m) and y-intercept (c) of the equation can be used to graph the line on a coordinate plane.

Direct Instruction (25 minutes):

• Show students how to use the slope and y-intercept to find two points on the line and graph it on the coordinate plane.
• Use several examples to illustrate the process, highlighting key steps and any common mistakes.
• Emphasize the importance of labelling the x and y axes and the importance of choosing appropriate scales.

Guided Practice (20 minutes):

• Distribute the handout or worksheet with practice problems.
• Work through a few problems as a class, providing guidance and feedback as needed.
• Have students work in pairs or small groups to complete the remaining problems, offering additional support as needed.

Independent Practice (15 minutes):

• Have students work independently on a set of additional problems, either from the handout or additional problems provided by the teacher.

Closure (10 minutes):

• Review key takeaways from the lesson, such as the steps for solving and graphing linear equations and the importance of labeling the axes and choosing appropriate scales.
• Address any remaining questions or confusion from students.

Assessment:

• Observe students as they complete the independent practice and offer feedback.
• Grade the handout or worksheet for accuracy and completion.

Note: This is just a sample lesson plan and can be adjusted based on the needs and abilities of your students. 

Worksheet 1. :

Worksheet 2 : 

Solving and Graphing Linear Equations Practice Problems

Objectives:

• To understand the concept of linear equations and their solutions.
• To practice solving linear equations.
• To practice graphing linear equations.

Instructions:

1. Solve the following linear equations: 

a. 2x + 3 = 7 

b. 5x - 1 = 12 

c. 3x + 2 = 10 

d. 4x - 6 = 18 

e. 6x + 4 = 14

2. Graph the following linear equations: 

a. y = 2x + 3 

b. y = -3x + 5 

c. y = 1/2 x - 1 

d. y = -4x - 2 

e. y = 3x - 5

3. Match the equations with their corresponding graphs: 

a. y = 2x + 3 

b. y = -3x + 5 

c. y = 1/2 x - 1 

d. y = -4x - 2 

e. y = 3x - 5

 Equations: a. y = 2x + 3 b. y = -3x + 5 c. y = 1/2 x - 1 d. y = -4x - 2 e. y = 3x - 5Graphs: i. __________ ii. __________ iii. __________ iv. __________ v. __________

4. Write the equation of the line that passes through the points (2, 3) and (4, 5).

5. Graph the equation from question 4 and identify the slope and y-intercept.

Answers:

1. a. x = 2 b. x = 2 c. x = 2 d. x = 3 e. x = 1
2. Graphs can be found by plotting points and connecting them.
3. a. y = 2x + 3 i. b. y = -3x + 5 ii. c. y = 1/2 x - 1 iii. d. y = -4x - 2 iv. e. y = 3x - 5 v.
4. The equation of the line is y = x + 1.
5. The slope of the line is 1 and the y-intercept is 1.