Lines are used and seen everyday! There are lines everywhere. When people think of a line, they usually think of a solid bar. The truth is that lines are made up of an infinite number of points that stretch infinitely in opposite directions. If you ask someone to draw a line, the will probably draw something like this: . This is wrong. A line, remember, stretches infinitely in opposite directions.
Vertical and Horizontal Lines.
Before getting to the complicated world of graphing lines with equations, first we will graph simple lines. A Coordinate Plane is used to graph lines on. It consists of a horizontal axis called the x-axis, and a vertical axis called the y-axis. The two lines meet at a point called the origin. The graph of X = 5 ( See fig. 1) would be a vertical line even though the x - axis is a horizontal line. The same for the graph of y = 5 ( See fig. 2), except that line would be horizontal while the y - axis is vertical. .
To graph a point on the coordinate plane, you need an ordered pair. An ordered pair is expressed as follows: (3, 4). The numbers inside tell you where to place the point. The first number represents the x-axis. It shows in which direction to move and how many units to move ( See fig. 3). The second number represents the y-axis. It too shows in which direction to move and how many units to move it ( See fig. 4). .
To graph, you first need an equation such as Y = 2x + 5 ( this type of equation will be covered in more detail). To compute a set of points to plot on the graph, a table of values must be used. In this table the x - value is a constant set of numbers. Plug in those numbers in place of the "x" in the equation Y = 2x + 5. Solve the equation for "y". Now that you have your table completed, plotting points can be used to construct a line. With the x/y values, ordered pairs such as (-3, -1) and (-2, 1) can be used in the graph.