Geometry Basics

Coordinate Plane

Two number lines set at 90 degrees from each other create a coordinate plane.

http://www.math.com/school/subject2/images/S2U4L1DP.gif


x-axis

The x-axis is the number line going left to right.  Positive numbers are on the right, and negative numbers are on the left.

y-axis

The y-axis is the number line going up and down.  Positive numbers are on the top, and negative numbers are on the bottom.

point

A point is a specific spot on the graph.

origin

The point where the x-axis and y-axis intersect.  It's ordered pair is (0,0).

ordered pair

The distance from the origin showing first to the left or right (x) then up or down (y).  The point (4,2) is right 4, up 2.

Line

A line is when two or more points are in a row.  Most people can draw a line based on two points, but in order to find other points on the line without using the graph, you need to understand the formula, which is y = mx + b.  Y is the dependent variable, X is the independent variable.  This means that all the X will have one and only one Y.  The other two letters help define the line.  b is called the y-intercept and shifts the graph up or down by that number.  m is called the slope and defines how fast the graph goes up.

Slope

To find the slope, you get two points.  Then you find the difference between the first and second in height, then the difference between the first and second in distance left or right from 0.

On this graph here, you can identify the following points: (-2, 1 ) (-1, 2) (0, 3) (1, 4) (2, 5)

To find the slope identify the distance between Y, then divide it by the distance between X.  So for (-2, 1) to (-1, 2), the distance between 1 and 2 is 1.  Then we divide it by the distance between -2 and -1 and we get 1.  1 divided by 1 is 1, so m = 1.  Then we identify where the line is when X is zero.  (0, 3).  So b = 3.  The line is y = 1x + 3.