Mathematics 8 - Linear Equations and Inequalities
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Questions and Answers

What is the standard form of a linear equation in two variables?

  • Ax + By < C
  • Ax + By = C (correct)
  • Ax + By > C
  • Ax + By ≥ C

    • Which symbol represents a linear inequality that is less than or equal to?

  • <
  • ≤ (correct)
  • ≥
  • >

    • What is the result of shading the region above the boundary line when graphing an inequality like y ≥ mx + b?

  • It indicates values are greater than the boundary line. (correct)
  • It indicates the boundary line is irrelevant.
  • It indicates values are less than the boundary line.
  • It indicates both equal and unequal values.

    • In the context of graphing linear inequalities, what type of line is drawn for inequalities using the less than (<) or greater than (>) symbols?

    <p>Dashed line</p> Signup and view all the answers

    When rewriting the inequality 3x + 2y < 6, what should be solved for to graph it?

    <p>y</p> Signup and view all the answers

    What is the primary difference between linear equations and linear inequalities?

    <p>Linear equations use an equal sign; linear inequalities use inequality symbols.</p> Signup and view all the answers

    Which of the following statements about the graph of linear inequalities is true?

    <p>It shows the complete solution set within half-planes.</p> Signup and view all the answers

    Why are A and B in the forms of linear equations and inequalities not equal to zero?

    <p>To avoid undefined slopes.</p> Signup and view all the answers

    What type of inequality can be expressed in the form $Ax + By < C$, $Ax + By > C$, $Ax + By ≤ C$, or $Ax + By ≥ C$?

    <p>Linear Inequality</p> Signup and view all the answers

    Which of the following represents a Linear Inequality in Two Variables?

    <p>$-5y ≥ 3$</p> Signup and view all the answers

    Which of the following best describes the graph of Linear Inequalities in Two Variables?

    <p>Half Plane</p> Signup and view all the answers

    A Linear Inequality in Two Variables can have how many solutions?

    <p>Infinite</p> Signup and view all the answers

    What is the name of the line that separates the plane into two regions in Linear Inequalities?

    <p>Plane Divider</p> Signup and view all the answers

    Which of the following is NOT a Linear Inequality in Two Variables?

    <p>$4 + 8x &lt; 14y$</p> Signup and view all the answers

    When will an inequality have a solid line as a plane divider?

    <p>When the symbol includes 'or equal to'</p> Signup and view all the answers

    What type of line should be drawn for the inequality y ≤ 2x – 1?

    <p>Solid line</p> Signup and view all the answers

    Which points are considered solutions for the inequality y ≤ 2x – 1?

    <p>(2, 3)</p> Signup and view all the answers

    When rewriting the inequality 2y – x ≤ 6, what is the first step?

    <p>Add x to both sides</p> Signup and view all the answers

    What does the inequality symbol '≤' indicate regarding the solutions of the boundary line?

    <p>Points on and below the line are solutions</p> Signup and view all the answers

    How do you determine the shaded region for an inequality graph?

    <p>By shading below the boundary line for '≤'</p> Signup and view all the answers

    What is the solution set of the inequality 2y – x ≤ 6?

    <p>y ≤ (1/2)x + 3</p> Signup and view all the answers

    Given the points plotted (-2, 2), (0, 3), and (2, 4), which point specifically does NOT satisfy y ≤ 2x – 1?

    <p>(2, 4)</p> Signup and view all the answers

    What is achieved by dividing both sides of the inequality 2y ≤ x + 6 by 2?

    <p>It simplifies to y ≤ (1/2)x + 3</p> Signup and view all the answers

    Which of the following equations is categorized as a Linear Inequality in Two Variables?

    <p>2𝑥 − 3𝑦 ≥ 9</p> Signup and view all the answers

    What is the first step to graph the inequality 𝑦 ≤ 2𝑥 - 1?

    <p>Rewrite the inequality to isolate ‘y’</p> Signup and view all the answers

    Which of the following points is included in the solution set of the inequality 𝑦 ≤ 2𝑥 - 1?

    <p>(0, -1)</p> Signup and view all the answers

    What is the correct value of ‘y’ when x = 1 in the equation y = 2𝑥 - 1?

    <p>1</p> Signup and view all the answers

    When graphing the inequality 𝑦 > -𝑥 - 5, the boundary line is plotted as which type?

    <p>Dashed line</p> Signup and view all the answers

    In the inequality 3𝑦 + 6𝑥 < 0, what can be said about the corresponding boundary line?

    <p>It is dashed.</p> Signup and view all the answers

    Which of the following must be true for a line representing the inequality 2𝑥 - 3𝑦 ≥ 9?

    <p>The line is solid.</p> Signup and view all the answers

    What is the significance of shading below the plane divider in the inequality represented by 'y ≤ 2 + 3'?

    <p>It shows the solutions where the inequality is satisfied.</p> Signup and view all the answers

    Which of the following points is a solution to the inequality '2y - x ≤ 6'?

    <p>(4, 2)</p> Signup and view all the answers

    What does the inequality 'y + 2 > x' imply about the relationship between y and x?

    <p>y can exceed x by any amount greater than 2.</p> Signup and view all the answers

    What is the first step in rewriting the inequality 'y + 2 > x'?

    <p>Subtract 2 from both sides.</p> Signup and view all the answers

    If the boundary line of an inequality is solid, what does it indicate about the solutions?

    <p>Solutions include points on the line.</p> Signup and view all the answers

    What does the statement 'y > 2x - 4' indicate about the solutions?

    <p>The solutions are above the line.</p> Signup and view all the answers

    Which of the following is a step to graph the inequality 'y > 2x - 4'?

    <p>All of the above.</p> Signup and view all the answers

    Which of the following points is a solution to the inequality y > 2x - 4?

    <p>(2, 3)</p> Signup and view all the answers

    Why are the points (1,1), (2,3), and (1,2) not solutions to the given inequality?

    <p>They are located on the boundary line.</p> Signup and view all the answers

    Which point does not satisfy the inequality '2y - x ≤ 6'?

    <p>(5, 8)</p> Signup and view all the answers

    When performing operations on inequalities, what must you remember?

    <p>You must reverse the inequality sign when multiplying or dividing by a negative number.</p> Signup and view all the answers

    What is the correct representation of the inequality when the values are shaded?

    <p>y &gt; 2x - 4</p> Signup and view all the answers

    Which of the following is NOT a characteristic of the inequality y > 2x - 4?

    <p>The boundary points are included.</p> Signup and view all the answers

    Given the inequality 5x - y < 2, what is the nature of the graph?

    <p>It is a diagonal line with dashed boundary.</p> Signup and view all the answers

    For which inequality does the solution include the boundary line?

    <p>y ≥ 9x + 3</p> Signup and view all the answers

    What is the graphical representation of 'x ≤ 3y + 5'?

    <p>Shaded region below the line.</p> Signup and view all the answers

    Study Notes

    Mathematics 8 - Learning Activity Sheet #1 (2nd Quarter - Week 1)

    • This document outlines concepts related to linear equations and inequalities in two variables.
    • Learning Competency: Differentiates linear inequalities in two variables from linear equations in two variables, and illustrates/graphs linear inequalities in two variables.
    • Background:
      • A linear equation in two variables is of degree one and written in the form Ax + By = C, where A, B, and C are real numbers and A and B are not both zero.
      • A linear inequality in two variables can be written as Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are real numbers, and A and B are not both zero. Linear inequalities use < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Inequality statements differ from equations by not using an equal sign.
    • Graphing Linear Inequalities in Two Variables:
      • Step 1: Rewrite the inequality so 'y' is isolated on one side.
      • Step 2: Graph the boundary line. A solid line is used for '≤' or '≥'; a dashed line is used for '<' or '>'.
      • Step 3: Shade the appropriate region. Shade above the line for '>' or '≥'; shade below the line for '<' or '≤'. The shaded area represents the solution set in the given inequality.
    • Activity Examples:
      • Examples show how to determine whether an equation is a linear equation or linear inequality.
      • Detailed steps on how to graph a linear inequality.
    • References and Resources: External links to helpful online resources concerning linear inequalities in two variables are provided.
    • Additional Activity (for study purposes): Multiple-choice questions on linear equations and inequalities in two variables. Covers topics such as determining whether something is linear equation or inequality, determining how to graph lines and inequalities, identifying solutions to inequalities, and the appropriate symbols used in inequalities.

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    LAS1_MATH_Week-1_Q2.pdf

    Description

    This learning activity sheet covers concepts related to linear equations and inequalities in two variables. Students will differentiate between linear inequalities and equations, as well as learn to graph these inequalities. It's an essential foundation for understanding algebraic relationships.

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