- GRAPHS and RECTANGULAR COORDINATES:
A GRAPH is a way of drawing a visual representation of a mathematical relationship.
Every graph uses a coordinate system. The most common coordinate system is called
RECTANGULAR COORDINATES.
(Rectangular coordinates are also called Cartesian coordinates because they were first used
by Rene Descartes, who wrote under his Latin name "Cartesius")
To start a graph using rectangular coordinates, take a piece of graph paper and draw a vertical axis
and a horizontal axis.
The point where the axes cross is called the origin.
- Rectangular Coordinates:
Every point on the graph corresponds to a pair of numbers, called coordinates.
The horizontal number is given first, followed by the vertical number.
The horizontal coordinate is usually called X. The vertical coordinate is usually called Y.
The horizontal coordinate (X) measures the distance to the right of the vertical axis.
Positive values of X are to the right of the vertical axis.
Negative values of X are to the left of the vertical axis.
The vertical coordinate (Y) measures the distance up from the horizontal axis.
Positive values of Y are above the horizontal axis.
Negative values of Y are below the horizontal axis.
The coordinates of the origin are, by definition, (0, 0).
- Quadrants:
First quadrant (upper right): X and Y are both positive. This quadrant is used the most.
Second quadrant (lower right): X is positive, Y is negative
Third quadrant (lower left): X and Y are both negative
Fourth quadrant (upper left): X is negative, Y is positive
- Slope:
Pick any two points along a line or curve. The difference in their Y values is called the rise.
The difference in their X values is called the run.
The Slope of the line (a very important concept) is defined as: slope = rise / run = difference in Y / difference in X
A positive slope means that an increase in X is accompanied by an increase in Y. As you move to the right, the line goes higher.
A negative slope means that an increase in X is accompanied by an decrease in Y. As you move to the right, the line goes lower.
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