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Linear Equations in Algebra
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Linear Equations in Algebra

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Questions and Answers

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

  • x^2 + y^2 = c
  • x + y = c
  • ax + by = c (correct)
  • ax - by = c
  • What is the purpose of the slope-intercept form of a linear equation?

  • To determine the slope of a line (correct)
  • To find the x-intercept of a line
  • To find the y-intercept of a line
  • To graph a linear equation on a coordinate plane
  • What is the standard form of a linear equation?

  • Ax - By = C
  • Ax + By = 0
  • Ax + By = C (correct)
  • Ax / By = C
  • What is the purpose of the addition and subtraction properties in solving linear equations?

    <p>To isolate the variable on one side of the equation</p> Signup and view all the answers

    What is the y-intercept of a line in the slope-intercept form?

    <p>The point where the line crosses the y-axis</p> Signup and view all the answers

    What is the definition of a linear equation?

    <p>An equation with a variable of degree 1</p> Signup and view all the answers

    Study Notes

    Linear Equations

    Definition

    • A linear equation is an equation in which the highest power of the variable(s) is 1.
    • General form: ax + by = c, where a, b, and c are constants, and x and y are variables.

    Types of Linear Equations

    • Simple Linear Equation: An equation with only one variable, e.g., 2x = 5.
    • Linear Equation in Two Variables: An equation with two variables, e.g., 2x + 3y = 7.

    Slope-Intercept Form

    • Slope-Intercept Form: y = mx + b, where:
      • m is the slope (a measure of how steep the line is).
      • b is the y-intercept (the point where the line crosses the y-axis).

    Standard Form

    • Standard Form: Ax + By = C, where:
      • A, B, and C are integers.
      • A is non-negative.
      • There are no fractions or decimals.

    Graphing Linear Equations

    • X-Intercept: The point where the line crosses the x-axis.
    • Y-Intercept: The point where the line crosses the y-axis.
    • Slope: The steepness of the line, which can be positive, negative, or zero.

    Solving Linear Equations

    • Addition and Subtraction Properties: Add or subtract the same value to both sides of the equation to isolate the variable.
    • Multiplication and Division Properties: Multiply or divide both sides of the equation by a non-zero value to isolate the variable.

    Linear Equations

    Definition

    • Linear equations have the highest power of variables as 1.
    • General form: ax + by = c, where a, b, and c are constants, and x and y are variables.

    Types of Linear Equations

    • Simple Linear Equation: one variable, e.g., 2x = 5.
    • Linear Equation in Two Variables: two variables, e.g., 2x + 3y = 7.

    Slope-Intercept Form

    • Slope-Intercept Form: y = mx + b, where:
      • m is the slope (steepness of the line).
      • b is the y-intercept (point where the line crosses the y-axis).

    Standard Form

    • Standard Form: Ax + By = C, where:
      • A, B, and C are integers.
      • A is non-negative.
      • No fractions or decimals.

    Graphing Linear Equations

    • X-Intercept: point where the line crosses the x-axis.
    • Y-Intercept: point where the line crosses the y-axis.
    • Slope: steepness of the line (positive, negative, or zero).

    Solving Linear Equations

    • Addition and Subtraction Properties: add or subtract the same value to both sides to isolate the variable.
    • Multiplication and Division Properties: multiply or divide both sides by a non-zero value to isolate the variable.

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    Quiz Team

    Description

    Learn about linear equations, their definition, types, and slope-intercept form. Understand the general form of linear equations and how to work with them.

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