Skip to main content
UploadLanguage (EN)Support
BusinessMobileSocial MediaMarketingTechnologyArt & PhotosCareerDesignEducationPresentations & Public SpeakingGovernment & NonprofitHealthcareInternetLawLeadership & ManagementAutomotiveEngineeringSoftwareRecruiting & HRRetailSalesServicesScienceSmall Business & EntrepreneurshipFoodEnvironmentEconomy & FinanceData & AnalyticsInvestor RelationsSportsSpiritualNews & PoliticsTravelSelf ImprovementReal EstateEntertainment & HumorHealth & MedicineDevices & HardwareLifestyle
Carlo Luna, profile picture
Uploaded byCarlo Luna
PPTX, PDF14,911 views

Math 8 - Linear Inequalities in Two Variables

This document is a math lesson plan on linear inequalities in two variables taught by Mr. Carlo Justino J. Luna at Malabanias Integrated School in Angeles City. The lesson introduces linear inequalities and their notation, defines them as having two linear expressions separated by symbols like greater than and less than, and shows examples of inequalities in two variables. It then discusses how to determine if an ordered pair is a solution by substituting into the inequality. Finally, it explains how to graph linear inequalities in two variables by first rewriting them as equations and then plotting intercepts and shading the appropriate region based on a test point.

Education◦
Downloaded 352 times
WELCOME to our Math Class LEARNING MATH IS fun-tastic MR. CARLO JUSTINO J. LUNA MALABANIAS INTEGRATED SCHOOL Angeles City
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 2 TheMathematician’sPrayer Heavenly Father, thankYou for all the blessingsYou gave unto us. Add joy to the world; Subtract evil from our lives, Multiply the good things for us; Divide the gifts and share them to others. Convert badness to goodness. Help us raise our needs toYou. Extract the roots of immoralities and perform our different functions in life. Tell us all that life is as easy as math. Help us all to solve our problems. These we ask in Jesus’ name, the greatest mathematician who ever lived on earth, Amen!
MATHEMATICS 8 Quarter 2 Week 1 Linear Inequalities IN TWO VARIABLES MR. CARLO JUSTINO J. LUNA MALABANIAS INTEGRATED SCHOOL Angeles City
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C LEARNING Competencies 4 » Differentiates linear inequalities in two variables from linear equations in two variables (M8L-IIa-2) » Illustrates and graphs linear inequalities in two variables » Solves problems involving linear inequalities in two variables (M8AL-IIa-4)
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C Initial Activity 5
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 6 GROUP ME! 3𝑥 + 5𝑦 = 10 𝑦 > 2𝑥 − 7 4𝑥 ≤ 𝑦 − 1 9𝑥 − 10𝑦 = 8 −2𝑦 < 𝑥 + 3 5𝑦 ≥ 𝑥 + 2 𝑥 + 𝑦 = 12 𝑦 = 2𝑥 − 5 𝑥 + 5𝑦 = 10 3𝑥 > 2𝑦 + 1 GROUP A GROUP B
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C GROUP A GROUP B 7 GROUP ME! 3𝑥 + 5𝑦 = 10 𝑦 > 2𝑥 − 7 4𝑥 ≤ 𝑦 − 1 9𝑥 − 10𝑦 = 8 −2𝑦 < 𝑥 + 3 5𝑦 ≥ 𝑥 + 2 𝑥 + 𝑦 = 12 𝑦 = 2𝑥 − 5 𝑥 + 5𝑦 = 10 3𝑥 > 2𝑦 + 1
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 8 GROUP ME! 3𝑥 + 5𝑦 = 10 𝑦 > 2𝑥 − 7 4𝑥 ≤ 𝑦 − 1 9𝑥 − 10𝑦 = 8 −2𝑦 < 𝑥 + 3 5𝑦 ≥ 𝑥 + 2 𝑥 + 𝑦 = 12 𝑦 = 2𝑥 − 5 𝑥 + 5𝑦 = 10 3𝑥 > 2𝑦 + 1 GROUP A GROUP B 3𝑥 + 5𝑦 = 10 9𝑥 − 10𝑦 = 8 𝑥 + 𝑦 = 12 𝑦 = 2𝑥 − 5 𝑥 + 5𝑦 = 10 4𝑥 ≤ 𝑦 − 1 −2𝑦 < 𝑥 + 3 𝑦 > 2𝑥 − 7 5𝑦 ≥ 𝑥 + 2 3𝑥 > 2𝑦 + 1 LINEAR EQUATIONS LINEAR INEQUALITIES
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 9 LINEAR INEQUALITIES IN TWO VARIABLES 3𝑥 + 5𝑦 = 10 9𝑥 − 10𝑦 = 8 𝑥 + 𝑦 = 12 𝑦 = 2𝑥 − 5 𝑥 + 5𝑦 = 10 4𝑥 ≤ 𝑦 − 1 −2𝑦 < 𝑥 + 3 𝑦 > 2𝑥 − 7 5𝑦 ≥ 𝑥 + 2 3𝑥 > 2𝑦 + 1 LINEAR EQUATIONS LINEAR INEQUALITIES LINEAR INEQUALITIES < – less than > – greater than ≤ – less than or equal to ≥ – greater than or equal to
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C LINEAR INEQUALITIES » Two linear expressions set that are separated by symbols >, <, ≥, ≤ 10 LINEAR INEQUALITIES IN TWO VARIABLES
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C » A linear inequality in two variables can be written in four forms: 𝐴𝑥 + 𝐵𝑦 > 𝐶 𝐴𝑥 + 𝐵𝑦 ≥ 𝐶 𝐴𝑥 + 𝐵𝑦 < 𝐶 𝐴𝑥 + 𝐵𝑦 ≤ 𝐶 where 𝐴, 𝐵, and 𝐶 are real numbers, 𝐴 ≠ 0 and 𝐵 ≠ 0 11 LINEAR INEQUALITIES IN TWO VARIABLES
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C » A linear inequality in two variables can be written in four forms: 𝐴𝑥 + 𝐵𝑦 > 𝐶 𝐴𝑥 + 𝐵𝑦 ≥ 𝐶 𝐴𝑥 + 𝐵𝑦 < 𝐶 𝐴𝑥 + 𝐵𝑦 ≤ 𝐶 where 𝐴, 𝐵, and 𝐶 are real numbers, 𝐴 ≠ 0 and 𝐵 ≠ 0 12 LINEAR INEQUALITIES IN TWO VARIABLES 4𝑥 ≤ 𝑦 − 1 −2𝑦 < 𝑥 + 3 𝑦 > 2𝑥 − 7 5𝑦 ≥ 𝑥 + 2 3𝑥 > 2𝑦 + 1 Examples:
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C » An ordered pair (𝑥, 𝑦) is a solution of a linear inequality in two variables if aTRUE statement results when the variables in the inequality are replaced by the coordinates of the ordered pair. 13 SOLUTION SET
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 14 SOLUTIONS OF AN INEQUALITY Determine whether each ordered pair is a solution of the given linear inequality. 5𝑥 − 2𝑦 ≥ 14 1. (3, −2) 𝑥 𝑦 5𝑥 − 2𝑦 ≥ 14 5(3) −2(−2) ≥ 14 15 +4 ≥ 14 19 ≥ 14 TRUE Therefore, (3, −2) is a solution of the given linear inequality. 𝑥 𝑦 5(0) −2(4) 0 −8 ≥ 14 −8 ≥ 14 FALSE Therefore, (0, 4) is not a solution of the given linear inequality. 2. (0, 4) 5𝑥 − 2𝑦 ≥ 14 ≥ 14
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 15 SOLUTIONS OF AN INEQUALITY Determine whether each ordered pair is a solution of the given linear inequality. 𝑥 < 𝑦 + 2 𝑥 < 𝑦 + 2 0 < 4 + 2 0 < 6 TRUE Therefore, (0, 4) is a solution of the given linear inequality. 1. (0, 4) 𝑥 < 𝑦 + 2 7 < −5 + 2 7 < −3 FALSE Therefore, (7, −5) is not a solution of the given linear inequality. 2. (7, −5) 𝑥 < 𝑦 + 2 −5 < 1 + 2 −5 < 3 TRUE Therefore, (−5, 1) is a solution of the given linear inequality. 3. (−5, 1)
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 16 SOLUTIONS OF AN INEQUALITY » Clearly, a linear inequality can have two or more solutions. » While the graph of 𝑥 + 𝑦 = 2 is a straight line, the graph of 𝑥 + 𝑦 > 2 is a half-plane. Linear Equation Linear Inequality The graph of a linear inequality in two variables is a HALF- PLANE. The shaded region consists of the points whose coordinates satisfy the inequality.
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C How do we graph linear inequalities in two variables? 17 Linear Inequality The graph of a linear inequality in two variables is a HALF- PLANE. The shaded region consists of the points whose coordinates satisfy the inequality.
GRAPHING Linear Inequalities
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 19 StepsinGraphingLinearInequalitiesinTwoVariables 1. Transform the linear inequality 𝑎𝑥 + 𝑏𝑦 > 𝑐 into linear equation 𝑎𝑥 + 𝑏𝑦 = 𝑐. 2. Determine the 𝑥- and 𝑦-intercept of the equation. 3. Plot and draw the boundary line. Use dashed lines (------) if the inequality is < or >. However, graph using solid lines ( ) if the inequality is ≤ or ≥, which means that the points on the line are included in the solution set. 4. Use the given inequality to choose a test point to be substituted in the given inequality in order to identify the shaded side of the boundary line. It is advisable to use (0, 0) for easy substitution of values. 5. If the resulting inequality isTRUE, shade the side that contains the test point. If the resulting inequality is FALSE, shade the other side of the boundary line.
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 20 Example 1: Graph 2𝑥 + 𝑦 ≤ 6. 2𝑥 + 𝑦 = 6 Rewrite the inequality as an equation. 2𝑥 + 𝑦 = 6 2𝑥 + 0 = 6 2𝑥 = 6 𝑥 = 3 𝑥-intercept is 3. Solve and plot the intercepts. 2𝑥 + 𝑦 = 6 2 0 + 𝑦 = 6 𝑦 = 6 𝑦-intercept is 6. The boundary is a solid line since the inequality symbol is ≤.
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 21 Example 1: Graph 2𝑥 + 𝑦 ≤ 6. 2𝑥 + 𝑦 ≤ 6 2 0 + 0 ≤ 6 0 ≤ 6 TRUE Pick a test point. Use (0,0) if possible. If the resulting inequality is TRUE, shade the side that contains the test point.
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 22 Example 2: Graph 𝑥 < −5. 𝑥 = −5 Rewrite the inequality as an equation. 𝑥 = −5 𝑥-intercept is −5. Solve and plot the intercepts. There is no 𝑦-intercept. The boundary is a dashed line since the inequality symbol is <.
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C 23 Example 2: Graph 𝑥 < −5. 𝑥 < −5 0 < −5 FALSE Pick a test point. Use (0,0) if possible. If the resulting inequality is FALSE, shade the side that does not contain the test point.
FACEMath L E A R N I N G M A T H I S F U N - T A S T I C Asynchronous/Self-LearningActivities Answer the following: Q2W1LC1A: • What I Know • What’s More • What I Can Do Q2W1LC1B: • What’s In • What’s More (items 1 & 2 only) Google Forms link • https://forms.gle/tiyr5aoZKo31v8aw8 24
MATHEMATICS 8 Quarter 2 Week 1 THANK You MR. CARLO JUSTINO J. LUNA MALABANIAS INTEGRATED SCHOOL Angeles City