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Wednesday 28th of June
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 Depdendent Variable

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 Dependent Variable

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The Cartesian Coordinate System

The Cartesian coordinate system consists of two real number lines placed at right angles to each other.

The horizontal number line is called the x-axis.

The vertical number line is called the y-axis.

The axes define a flat surface called the xy-plane.

Every point in the xy-plane has two numbers associated with it.

â€¢ The x-coordinate or abscissa tells how far the point lies to the left or right of the y-axis.

â€¢ The y-coordinate or ordinate tells how far the point lies above or below the x-axis.

The x-coordinate and the y-coordinate are often written inside parentheses, like this: (x, y).

The first number, x, represents the x-coordinate and the second number, y, represents the y-coordinate.

For example, the point that is 3 units to the right of the y-axis and 6 units below the x-axis is labeled (3, -6).

Because the order in which the pair of numbers is written is important, (x, y) is called an ordered pair. Thus, the point (-6, 3) is not the same as the point (3, -6).

The x-axis and the y-axis intersect at the point (0, 0). This point is called the origin.

The x-axis and the y-axis divide the xy-plane into four regions called quadrants.

 Quadrant I II III IV Sign of x positive negative negative positive Sign of y positive positive negative negative

A point on an axis does not lie in a quadrant.

Example 1

Find the coordinates of each point labeled on the graph.

Then, state the quadrant in which each point lies.

Solution

Point A has coordinates (2, 5), and lies in Quadrant I.

Point B has coordinates (3, -4), and lies in Quadrant IV.

Point C has coordinates (-5, 3), and lies in Quadrant II.

Point D has coordinates (-6, -2), and lies in Quadrant III.

Point E has coordinates (5, 0). It is not in a quadrant since it lies on the x-axis.

Example 2

Plot each point on a Cartesian coordinate system:

a. (5, -4)

b. (-4, 6)

c. (-3, 0)

d. (0, -3)

Solution

The plot the point (5, -4), start at the origin:

â€¢ move 5 units to the right;

â€¢ then move down 4 units;

â€¢ place a dot at this location.

Follow a similar procedure for the other points. Notice the difference between the locations of points (-3, 0) and (0, -3).