Cartesian Coordinates and Graphing
On a map, you use latitude and longitude to find a location. On a coordinate plane, you use ordered pairs (x, y) to do the same thing. The x-coordinate says 'how far right' and the y-coordinate says 'how far up'.
The coordinate plane
Two perpendicular number lines: the x-axis (horizontal) and y-axis (vertical). They intersect at the origin (0, 0). The plane is divided into four quadrants: I (upper right, +x, +y), II (upper left, −x, +y), III (lower left, −x, −y), IV (lower right, +x, −y).
Ordered pairs and plotting
An ordered pair (x, y) specifies a point. Start at the origin, move x units along the x-axis (right if positive, left if negative), then move y units parallel to the y-axis (up if positive, down if negative). Example: (3, −2) is 3 units right, 2 units down.
Graphing linear relations
If y = 2x + 1, create a table of values: x = −1 gives y = −1 (point (−1, −1)); x = 0 gives y = 1 (point (0, 1)); x = 1 gives y = 3 (point (1, 3)). Plot these points and connect them to see the line.