Introduction to linear equations

Introduction to linear equations

This is a lesson that teaches how to determine if an expression is a linear equation; and how to graph a linear equation.
Basic Concepts: Representing patterns in linear relations, Reading linear relation graphs, Solving linear equations by graphing, Identifying functions
Related Concepts: System of linear equations, Graphing linear inequalities in two variables, Graphing systems of linear inequalities

Lessons

Expression: A collection of numbers, variables, and signs, such as 3,3x+4,5x2+2,x−3, 3, 3x+4, 5 x^2 + 2, \sqrt{x-3}, etc

Equations: A mathematical statement with an equal sign, such as y=2,y=3x−2,y=x,x=3, y = 2, y = 3x-2, y = x, x = 3, etc

Linear
Equation: Ax + By = C (A, B & C are constants; x & y are variables)
All linear equations are functions except a vertical line such as x = 3.
  • Introduction
    a)
    What is a linear equation?

  • 1.
    Which of the following is a linear equation?
    i)
    x = 4
    ii)
    y = 2
    iii)y = 3x + 5
  • 2.
    Graph the linear equations:
    a)
    y = -34 {3 \over 4} x + 2

    b)
    y = 45 {4 \over 5} x−2 -2

    c)
    34x+0.6y=3{3 \over 4}x + 0.6y =3

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3.
Points, Lines, Segments, Midpoints and Chords
3.1
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
3.2
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
3.3
Slope-Y-intercept form: y = mx + b
3.4
Graph using a single point and slope
3.5
Solve linear equations
Geometry
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