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Operant Conditioning 
Positive reinforcement
principles of operant conditioning
basic processes in operant conditioning positive reinforcement strengthen mindbodysoulheart happiness health Love passion 








Coordinate Graphing

Coordinate graphing sounds very dramatic but it is actually just a visual method for showing relationships between numbers. The relationships are shown on a coordinate grid. A coordinate grid has two perpendicular lines, or axes, labeled like number lines. The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the x-axis and y-axis intersect is called the origin.

The numbers on a coordinate grid are used to locate points. Each point can be identified by an ordered pair of numbers; that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. Ordered pairs are written in parentheses (x-coordinate, y-coordinate). The origin is located at (0,0). Note that there is no space after the comma.
The location of (2,5) is shown on the coordinate grid below. The x-coordinate is 2. The y-coordinate is 5. To locate (2,5), move 2 units to the right on the x-axis and 5 units up on the y-axis.

The order in which you write x- and y-coordinates in an ordered pair is very important. The x-coordinate always comes first, followed by the y-coordinate. As you can see in the coordinate grid below, the ordered pairs (3,4) and (4,3) refer to two different points!

The function table below shows the x- and y-coordinates for five ordered pairs. You can describe the relationship between the x- and y-coordinates for each of these ordered pairs with this rule: the x-coordinate plus two equals the y-coordinate. You can also describe this relationship with the algebraic equation x + 2 = y.
x-coordinatex + 2 = yy-coordinateordered pair
00 + 2 = 22(0,2)
11 + 2 = 33(1,3)
22 + 2 = 44(2,4)
33 + 2 = 55(3,5)
44 + 2 = 66(4,6)
To graph the equation x + 2 = y , each ordered pair is located on a coordinate grid, then the points are connected. Notice that the graph forms a straight line. The arrows indicate that the line goes on in both directions. The graph for any simple addition, subtraction, multiplication, or division equation forms a straight line.





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