Graphs of Linear Equations in Two Variables

Grade 8 · Mathematics

Semester 1 | Period 3 | Week 16

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Subject: Mathematics

Semester: 1

Period: 3

Week: 16

WEEK 16
Class: Grade 8
Age: 13 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Graphs of Linear Equations in Two Variables

SPECIFIC OBJECTIVES:
By the end of the lesson, pupils should be able to:

  1. Understand and define linear equations in two variables.
  2. Plot the graphs of linear equations on the Cartesian plane.
  3. Solve word problems that lead to linear equations.
  4. Apply knowledge of linear equations to real-life situations.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Graphing exercises
• Word problems
• Discussions

INSTRUCTIONAL MATERIALS:
• Graph paper
• Whiteboard and markers
• Ruler
• Flashcards with equations
• Graphing software (optional)

 

PERIOD 1 & 2: Graphs of Linear Equations in Two Variables

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains linear equations in two variables and the meaning of the equation.

Pupils listen and ask questions.

Step 2 - Explanation

Defines a linear equation (e.g., y = 2x + 3) and explains how to plot it on the graph.

Pupils take notes.

Step 3 - Demonstration

Uses graph paper and ruler to plot points of a linear equation.

Pupils practice plotting equations.

Step 4 - Practice

Pupils solve and plot several linear equations.

  

Pupils work on practice problems. |

NOTE ON BOARD:

  • Linear equation: y = mx + b
    where m is the slope, and b is the y-intercept.
    Example: y = 2x + 3
    Slope = 2, y-intercept = 3

EVALUATION (5 exercises):

  1. Plot y = x + 4.
  2. Plot y = 3x – 2.
  3. Plot y = -x + 5.
  4. Plot y = -2x – 3.
  5. Plot y = 0.5x + 1.

CLASSWORK (5 questions):

  1. Plot the equation y = 2x – 3.
  2. Find the graph for y = x + 5.
  3. Plot y = -x + 1.
  4. Graph y = 2x + 2.
  5. Plot y = -3x + 4.

ASSIGNMENT (5 tasks):

  1. Plot y = x – 2.
  2. Solve and graph y = -2x + 6.
  3. Plot y = 0.5x – 1.
  4. Graph y = -x + 3.
  5. Solve for y in the equation y = 2x + 4 and plot the graph.

 

PERIOD 3 & 4: Word Problems Involving Linear Equations

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains how to translate word problems into linear equations.

Pupils listen and ask questions.

Step 2 - Explanation

Demonstrates solving word problems such as finding cost, profit, or distance.

Pupils follow along and take notes.

Step 3 - Problem-Solving

Solves a word problem involving linear equations.

Pupils solve individual problems.

Step 4 - Practice

Pupils solve word problems independently.

Pupils work on practice word problems.

EVALUATION (5 exercises):

  1. A car travels at 60 km/h. How far will it travel in 5 hours? (Use the equation distance = speed × time).
  2. The total cost of a pizza is given by the equation C = 2x + 5, where x is the number of pizzas. If x = 4, what is the cost?
  3. A company earns 3x + 200 from selling x items. How much does it earn when x = 10?
  4. A train moves at a constant speed of 80 km/h. Write the equation for distance and solve for distance at 4 hours.
  5. The equation for profit is P = 100x – 50. What is the profit when 20 items are sold?

CLASSWORK (5 tasks):

  1. Translate the problem into an equation: A ticket costs 2x + 3. If x = 5, how much does a ticket cost?
  2. A store sells pencils for x + 1. What is the total cost for 3 pencils?
  3. Translate this into a linear equation: A team scores 3x + 10 points in a match. What is the total score if x = 4?
  4. A family spends x + 100 on groceries. What is the total cost for x = 2?
  5. Solve for total distance traveled: A cyclist travels at 15x speed. Find distance at x = 5 hours.

ASSIGNMENT (5 tasks):

  1. Write and solve a linear equation for the total distance a runner travels at 6 km/h for 3 hours.
  2. Translate the word problem: A taxi charges 50x + 30 for a ride. What is the cost if x = 3?
  3. Write an equation for a savings account balance: Balance = 2x + 100, solve for x = 4.
  4. Translate into a linear equation: A bank pays interest of 5x + 20. Find the payment for x = 10.
  5. Write and solve a linear equation: A family’s rent is x + 3000 per month. Find the rent for x = 5.