Graphing Equations

Graphing equations is the heart of Algebra! Especially graphing linear equations, which will be the focus of this unit.

You'll find that when working with those impossible word problems, a graph can give you an unbelievable amount of information and help you to solve the problem more easily.

You'll also find that linear graphs are used in many real world situations.

So, get your graph paper, ruler, and pencil ready and let's get started graphing.

Use the table of contents below for help on a particular method, or follow along lesson by lesson for a complete unit on graphing equations.

Graphing Equations Unit



In this unit, you will be graphing linear equations.  So, before we get started with all of the lessons above, I'd like to briefly introduce you to linear equations and review how to graph points on a coordinate plane,


So, what exactly is a linear equation?

An equation is defined as linear when it's graph presents a straight line. These equations contain terms that are either a constant and/or the product of a constant and a single variable to the first power. A linear equation can have more than one variable.


Examples of Linear Equations

Examples of linear equations

Before you get started, let's just do a quick review of how to graph points on a coordinate plane!


Brief Overview of Graphing on a Coordinate Plane

A coordinate plane is a graph formed by two number lines.

There is a horizontal number line called the x-axis.

There is also a vertical number line called the y-axis.

Coordinate Plane with x-axis, y-axis, and origin labeled

The origin is where the x-axis and y-axis intersect. This point is (0,0).

You can locate any point on the graph using ordered pairs. An ordered pair is made up of 2 numbers, an x-coordinate and a y-coordinate. It is always written inside of parentheses.

(x-coordinate, Y-coordinate)


Let's Look at an Example

Let's graph the point (2,3)

On a graph, start from the origin (0,0) and count to the right on the x-axis to 2, and up to 3 on the y-axis).

Graphing Points on a coordinate plane


If you haven't graphed points on a coordinate plane in a while, it might be a good idea to practice before you start the Algebra lessons.


Practice Graphing Points on a Coordinate Plane

Graph the following points on the coordinate plane: 

1. (3,5)

2. (-2,-1)

3. (-4, 1)

4. (0,-5)

5. (6, 0)


Solution

Answer Key for graphing points on a coordinate plane.

If you can graph these points on a coordinate plane, then you are ready to start learning how to graph linear equations!

Move onto the next lesson on Graphing Using a Table of Values

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