 2.2 Plotting Points and Reading Coordinates
On page 2.1, we plotted a point which had the value 4 on the x-axis and 2 on the y-axis, the coordinates 4 and 2.  When you state a point’s position in a coordinate system, you usually always begin with the horizontal axis, the x-axis.  After that you indicate the y-value, the position on the y-axis.  This is written (4, 2) and can be read as:

• ”the point 4, 2”
• ”a point with the coordinates 4 and 2”
• ”a point with the x-coordinate 4 and y-coordinate 2”.
You usually also name the point with an upper case letter. If we give the point (4, 2) the name P, it would be written P(4, 2). If you are going to plot a point in a coordinate system, you can use the method below.  We will take a new example where the
x-coordinate is -4 and the y-coordinate is 2, (-4, 2).

1. We begin with the x-coordinate, the horizontal axis. Because the
x-axis is -4, we look for the -4 on the x-axis. We know that our point will lay somewhere along this dotted line because it shows where the x-value is -4.  We know that the y-value is 2, and then can even plot that in the coordinate system. Now you have two dotted lines, one that shows -4 on the x-axis and another that shows 2 on the y-axis.  Both of these lines intersect at a point.  The points position is (-4, 2) because we always begin by indicating the x-value.

These red lines which we have drawn in order to be able to see where the point ends up are usually not drawn when we indicate a coordinate.   