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 (C)</p>
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What is the y-intercept of a line in the slope-intercept form?

<p>The point where the line crosses the y-axis (A)</p>
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What is the definition of a linear equation?

<p>An equation with a variable of degree 1 (A)</p>
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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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