Fig.1. Graph Coordinates
STRAIGHT LINE GRAPHS INTRODUCTION
The graph plane is like a mathematical canvas where the graph is drawn. The graph plane is also called the Cartesian Plane after French mathematician Rene Descartes. It is a 2 dimensional plane with 2 axis (a third axis can be added for 3 dimensional work). The y-axis is vertical and the x-axis horizontal. Using a set of points or 'coordinates' any point in the plane can be described (plotted).
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SOME EXAMPLES OF lINEAR (STRAIGHT LINE) GRAPHS
Let's look at an example of how to draw a linear graph (straight line graph). We will use two methods, 1. using tables and 2, using a combination of y=mx +c and rise over run. The following table is done vertically but you should also be able to complete it horizontally.
Sketch the graph of y = 2x + 1
Sketch the graph of y = 2x + 1
1) Create a table like the one above. It will give enough information to 'build' the graph. Substitute each value of x into the equation y = 2x +1 to get the value of y. This will produce a set of coordinates that can be plotted on the graph.
2) Plot the coordinates on the graph. Notice the pattern of 'rising' up 2, go across 1, rise up 2, go across 1 etc. as you climb up a 'staircase'. When you can't go any further, work backwards to complete the graph in the lower left part of the Cartesian plane.
Connect the dots with a line and arrow heads to finish. A good graph should cover as much of the graph space as possible.
Using y = mx + c to sketch the graph. m stands for slope or gradient and c, represents the y intercept of the line (where it cuts the y-axis). Compare with y = 2x + 1 The value of c is 1, so locate the point on the y-axis at 1. This just happens to be the location (0,1). The slope 'm' is 2, the number in front of the x term, so locate the next point by moving up 2 and across 1 as in the diagram so that you land on the point (1,3). |
Follow this pattern in either direction until you reach the extremes of the graph (run out of space). The graph will be the same as the one in Fig.6.