Graphing on a Cartesian Coordinate System

Coordinates on the Real Number Line


 The Real Number line organizes points around the center zero. Each number has two elements.

  • The sign of a number indicates whether the number lies to the left or the right of zero. Positive numbers are numbers without a (-) sign in front them such as 2, 5, 12.4, etc. Positive numbers lie to the right of zero. Negative indicates are numbers that have a (-) sign in front of them such as -4,-12, -4.31, etc. Negative numbers lie to the left of zero.

  • The size of a number indicates the distance from zero.

Example:


Find the number x = 5 on the number line.

Solution:


  • The sign of 5 is positive so the number lies to the right of zero.

  • The size of the number is 5 which indicates that the distance from zero is 5 units.


Using these two data, we can place the point x=5 on the following number line.



Example:


Find the number x = -3 on the number line.

Solution:


  • The sign of -3 is negative so the number lies to the left of zero.

  • The size of the number is 3 which indicates that the distance from zero is 3 units.



Using these two data, we can place the point x = -3 on the following number line.



To see various other points on the numberline, click the button associated with the value of x that you would like to see.




Now, practice yourself by clicking the number line on the indicated value of x.


If the Real Number line is oriented vertically, the two elements of a number y are as follows.

  • The sign of a number indicates whether the number lies above or below zero. Positive numbers are above zero. Negative numbers are below zero.

  • The size of a number indicates the distance from zero.



Practice this concept below!



The Cartesian Coordinate System



 The Cartesian Coordinate System combines the the x numberline and the y numberline. If we start at the center of our grid which is called the origin, the value for x is the number of units to the right/left that we move. The value for y is the number of units up and down that we move. Using x and y together we can obtain any location or point (x,y) in the cartesian plane. Click on any point to see the associated coordinates (x,y) of the point.





In the above example, we saw coordinates (x,y) when both x and y are integers. In fact, there is no need for x and y to assume integer values. Click on any point to see the associated coordinates (x,y) of the point.

You've seen us do it. Now try it yourself by clicking on the point associated with the given x and y values.!