Know the terminology: rectangular coordinate system, ordered pair, coordinates, origin, x and y-axis, quadrants, standard form, x and y-intercepts, horizontal and vertical lines.

x/y chart:  This is a way of finding points on the line so that you can connect the dots and draw the line. Just plug in any number for x and solve for y (or vice versa).  Each of the x,y pairs that you find are an ordered pair (a point on the graph). Example 1 explains this process very well.

Horizontal & Vertical Lines: 

Concept: A horizontal or vertical line "crosses" the x or y axis at a right angle.
If the equation is y = 2, find the 2 on the y-axis and draw a point there, then draw a line that "crosses" the y-axis at that point. (Think of a "+" shape, see graph on p. 130, Figure 5). The y-axis is one stick of the "cross" and your line is the other stick. 
If the equation is x = - 1 , go to the x-axis, find (-1) and draw a point there, then make your "cross" shape (see the graph in Figure 6). 

Finding x & y intercepts:  The x-intercept is the point where your line intercepts (or passes through) the x-axis.
In example 5, figure 7, the x-intercept is at the origin.  
The y-intercept is the point where your line intercepts the y-axis. In figure 7, the y-intercept is also at the origin.

Concept: Since the x-intercept is on the x-axis, the value of y at that point is zero, and for the y-intercept, the value of x at that point is zero. 

The above concept is used to find the x and y-intercepts. To find the x-intercept, plug y = 0 into the equation. To find the y-intercept, plug x = 0 into the equation.  Normally this would give you two different points which you would draw and connect to make your line.  However, in this example the two intercepts happen to be the same point so they had to go back to the x/y chart and find a second point.