Straight line graphs are the most basic graph type to draw and to evaluate. Before we draw a few its important to cover the coordinate system that makes it possible to sketch graphs.
Rectangular or Cartesian Coordinate System
The rectangular coordinate system was developed by the French Mathematician Rene Descartes. Most graphs can be plotted using this system.
Straight Line Graphs
The general equation for a straight line graph is a simple linear equation.
Where …. a, b and c are constants.
This equation can be written in a standard form called the gradient – y – intercept formula
- m is the gradient and c is the y-intercept
You only require two points to sketch a straight line graph thus making the calculations very simple. Two points that are always possible to find are where your graph cuts the y-axis and x-axis.
Luckily for us these points occur when the y and x values are zero.
- When y = 0 then we would get the x-intercept
- When x = 0 then we would get the y-intercept
Sketch the following straight line graph
We only require two coordinate points to sketch the straight line graph
Next is to find the second point….
With both points now calculated its a simple matter of plotting the graph on the Cartesian plane.
Important Straight Line Graph Characteristics
- If two or more straight line graphs are parallel to one another then their gradients are equal. Therefore the value m in all the graph equations will be equal.
- If two straight line graphs are perpendicular to one another then the multiplying their gradients will yield an answer of -1
- If c = 0 then one point of the graph will pass through the origin
- The gradient of the graph is basically the change of the y values over the change in the x values over a certain distance. This can be represented as
Find the gradient of the graph for the given pair of coordinates (3, -7) and (10, 7)
Make use of the following formula
Substituting in your coordinates will then yield your gradient.
Straight line graphs are the most basic graphs used in engineering. Thus knowing how to solve for all the related data points is important.