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The Coordinate Graphing System

In this lesson, you will be learning about how perpendicular number lines are used to define a coordinate graphing system.

Perpendicular Lines are lines that cross to form four right (90º) angles.

Number lines are lines which have been divided into equal parts which are numbered at regular intervals, in the same way as a ruler is divided and marked.

Integers are all the positive whole numbers, their opposites (the negative values of each number), and zero.

Learning Outcomes

By the end of this lesson, your children will have a basic understanding of how a coordinate graphing system is arranged, and be able to identify its parts using the correct mathematical terminology.

Warm Up

Coordinate graphing is an area where algebra and geometry overlap one another. Since most students tend to identify more with one of these areas than the other, coordinate graphing is often a subject of shared interest among students.

Those who enjoy algebra more appreciate the functions and the visual display of patterns. Those who enjoy geometry more seem to understand the patterns better by plotting points and drawing lines to create the coordinate graph. Since this is an area of overlap, it is especially important to understand how the coordinate graph system is arranged, and what all the various parts are called.

Understanding the academic vocabulary involved in particular math concepts helps make sure that all mathematicians share a common, basic understanding. Take the Pre-Test below. If you score 10 or more, you are ready to go on to the lesson.

Pre-assessment worksheet

Have your children take the Pre-Test below to see if they are ready for this lesson. If they get 9 or less correct, review number lines and types of lines with them before continuing on to the lesson.

Main Lesson: Coordinate Graphing System

The coordinate graphing system is formed by a pair of perpendicular number lines. The two lines intersect, or cross, to form four right angles.

Graph Quadrants

If you look at the coordinate graph, you can see that when the x and y axes cross, they form four sections. These sections are called quadrants. That’s why you will sometimes hear a coordinate graph be called a four-quadrant graph. The quadrants are numbered using Roman numerals, starting with the top right quadrant, and moving around in a circle to the left.

Remind your children that the x axis coordinate is listed first in the ordered pair, followed by the y axis coordinate. The numbers in every ordered pair will follow the (x ,y) format.

Work through the five questions below with your children to help them recall what they have learned in this lesson.

1. What kind of lines form a coordinate graphing system?
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Perpendicular lines form the coordinate graphing system.

2. What is the vertical line called?
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The y axis

3. What is the horizontal line called
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The x axis

4. How do you know whether to go right or left from zero on the x axis?
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If the x number is positive, go right. If it is negative, go left.

5. What are the numbers that give the coordinates of a point called?
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The coordinates of a point are called an ordered pair.

Note: You might find this printable graph paper generator handy.


  • The coordinate graphing system is formed by the intersection of two perpendicular number lines marked by integers.
  • The lines are called the x and y axes.
  • The x axis is horizontal.
  • The y axis is vertical.
  • The origin is the point at which the lines intersect.
  • The intersecting lines form four sections, called quadrants, numbered with Roman numerals.
  • The coordinates are written as an ordered pair.
  • The ordered pair is always written in the (x, y) format.
  • Always begin at the origin when plotting a point.

Test Questions

Review the above recap points with your children and then print out the Post Test that follows.

At least 8 out of 10 correct will show that your children have completed this unit with sufficient understanding to move on to the Coordinate Graphing of Real-World Situations.

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  • "The Coordinate Graphing System". Helping with Math. Accessed on July 18, 2024. https://helpingwithmath.com/the-coordinate-graphing-system/.

  • "The Coordinate Graphing System". Helping with Math, https://helpingwithmath.com/the-coordinate-graphing-system/. Accessed 18 July, 2024.

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