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## Introduction

There is an old saying that says “a picture is worth a thousand words.”  This saying holds true in mathematics whenever you can use a graph to represent mathematical information.  Graphs can be used to compare and identify many different types of information and have a lot of different uses in the real world.  A scientist can use a graph to show the population density of an endangered animal, compare speeds of different objects in experiments, and chart temperatures all around the globe.  A sports magazine can use graphs to show batting averages, compare points scored in different situations, and even judge their own circulation.

In mathematics, graphs are used to show a visual image of equations or other functions.  All of the possible uses of graphs that were mentioned above rely on the basic mathematical building blocks that will be described in this lesson and the lessons that follow.  In Algebra, most graphs are drawn using the letters x and y.  These letters are used most often because two-variable equations most commonly contain the variables x and y.  These letters can represent any comparison that you want them to when doing a graph.  They can compare time vs. money, height vs. weight, time vs. distance, pennies vs. nickels, boys vs. girls, etc.

## Lesson

One of the simplest comparisons that can be graphed is that of a straight line.  Consider the equation y = 2x + 1.  There are many possible combinations of x and y that work in this equation.  One way to demonstrate the combinations is to simply make a big list of them.  However, all the possible working combinations can be shown on a single graph that compares x and y.  This graph looks like this:

The red line on the graph above represents every possible solution for the equation y = 2x + 1.  Each pair of numbers (x and y) that work for the equation can be shown with a point on the line.  Any point on the line is called a solution.  Here are three of the solutions for this equation:

The diagram that the line is drawn on is called a coordinate plane.  It is simply made up of a horizontal line (called the x-axis) and a vertical line (the y-axis).  The central point of the diagram is the point where the lines intersect (called the origin).  A coordinate plane has two dimensions and can be thought of as being flat like a piece of paper or a tabletop.

Points can be placed anywhere on the coordinate plane.  For example, they can be used to compare the ages and heights of individuals in a health study.  Since age and height must both be positive numbers, we can zoom in on the top right section of the graph (or first quadrant) in order to display the information.

Each dot on the graph is called a point, and each of the points represents the age and height of a single person.  Even though the exact ages and heights are not shown on the graph, it is obvious that the graph is trending upward.  In other words, as the age of a person increases, the person grows so the height also increases.  This is generally true of humans as they grow to reach maturity, but it is not always the case.  You may know people who are older than you but are also short.  However, even those people are generally taller than a toddler or small child.

We will explore points more in the lesson plotting points on the coordinate plane.  For now, you should be able to identify the major parts of the coordinate plane.

## Try It

1) Physical objects can be described as one dimensional, two dimensional, and three dimensional.  Which of these best describes a coordinate plane?

2) What is the name of the horizontal line in a coordinate plane?

3) The intersection point of the two lines in a coordinate plane is called the .

4) What does the y-axis look like?

Scroll down for solutions...

Solutions:

1) A coordinate plane is two dimensional.

2) The horizontal line is called the x-axis.

3) The intersection of the two lines in a coordinate plane is the origin.

4) The y-axis is a vertical line that goes up and down through the middle of the graph.

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