Description

Another skill that is explore in Algebra is the concept of the rectangular coordinate system, plotting points and graphing. Here, we explore the foundations of this topic including Exploring the Rectangular (Cartesian) Coordinate System, graphing linear equations in two variables, understanding the slope of a line and equations of lines; graphing linear inequalities in two variables and exploring relations, functions, and function notation.

Sections of this topic include:

1. The Rectangular (Cartesian) Coordinate System

   Another application of Algebra is to be able to plot points and graph equations in a Rectangular or Cartesian Coordinate System. Groups in this section include determining quadrants where points are located; finding ordered pairs from descriptions of points; plotting points on a rectangular coordinate system; using a rectangular coordinate system to explore plotting points; determining an equation from plotting points; using an equation to complete ordered pairs.

2. Graphing Linear Equations in Two Variables

   We improve our knowledge of how to graph lines by learning techniques in graphing linear equations in two variables. Groups in this section include graphing linear equations by finding the x- and y- intercepts; graphing linear equations by finding three ordered pairs; finding linear equations then graphing by finding three ordered pairs; and completing ordered pairs then graphing.

3. The Slope of a Line; Equations of a Line

   With a foundation of graphing linear equations of two variables, we explore easier ways to graph lines and to find equations of lines given either a slope and a point or two points. Groups in this section include finding slopes of a line through a pair of points; graphing linears through a given point with a given slope; finding equations of lines given a point and a slope; and finding equations of lines given two points.

4. Graphing Linear Inequalities in Two Variables

   If we can graph linear equations in two variables, why not graph linear inequalities in two variables? Groups in this section include graphing linear inequalities in two variables; writing inequalities to describe regions; writing descriptions of regions defined by sets.

5. Relations; Functions; and Function Notation

   Building on our knowledge of equations of two variables and graphing, we explore a more advanced concept, functions. Groups in this section include determining if a relation is a function; finding domains and ranges of functions; finding domains of non-linear functions; evaluating functions; graphing functions.