Straight Line Graphs

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.
Graph

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

Where:

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.
Therefore

When y = 0 then we would get the x-intercept
When x = 0 then we would get the y-intercept

Example 1

Sketch the following straight line graph

Solution

We only require two coordinate points to sketch the straight line graph
x- coordinates

Next is to find the second point….
y-coordinate

With both points now calculated its a simple matter of plotting the graph on the Cartesian plane.
Graph

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