Linear Equations

Equations

statements that two expressions are equal

Linear Equations

each variable is raised to the power of 1 (not higher) and without products of variables

Equivalent

two equations that have the same solution

The Number Line

geometric approach

representation for numbers: ℝ

The Cartesian Plane

2D generalization of the number line: ℝ²

• horizontal axis: 𝑥-axis

• vertical axis: 𝑦-axis

• each point is an ordered pairs of numbers: Point (𝑥, 𝑦)

• Point (0, 0): the origin

3D Space

A generalization of the 2D Cartesian plane: ℝ³

three orthogonal axes: x, y and 𝑧

each point is an ordered 3 tuple of numbers: Point (x, y, z)

Point (0, 0, 0): the origin