Graphs of Linear Equations

Graphs of linear equations are straight lines.

Steps to drawing the graph of a linear equation (y = mx + c where c is the y-intercept when x = 0 and m is gradient):
1. Construct a table of values of x and y. You will need the coordinates of at least two points. 
2. Choose a suitable scale.
- The scale used on the x-axis does not have to be the same as the y-axis. 
- The scale chosen should allow for the largest possible graph to be drawn. 
- The bigger the graph, the more accurate will be the results obtained from it. 
3. Plot the points on the graph paper and draw a straight line through all the points. 
4. Label your graph with the equation of the line. 

Different types of linear graphs include:
1. The graph of a horizontal line passing through the point (0, c) and parallel to the x-axis is of the form : y = c.
Gradient of the graph of the form y = c is zero. 

2. The graph of a vertical line passing through the point (a, 0) and parallel to the y-axis is of the form : x = a.
Gradient of the graph of the form x = a is undefined. 

3. The graph of a straight line passing through the origin, (0, 0), and with gradient m is of the form : y = mx, where m is a constant. 
If the gradient, m, is positive, the line slopes upwards to the right. 
If the gradient, m, is negative, the line slopes upwards to the left. 
The larger the numerical value of m, the steeper the line. 

4. The graph of a straight line that cuts the y-axis at the point (0, c) and has gradient m is of the form : mx + c.
When the value of m remains the same with c taking on different values, the graphs are parallel lines cutting the y-axis at the points (0, c). 

Note:
To check whether the point (4, 5) lies on the line y = 2x - 3, substitute the value of x = 4 into the equation. If it lies on the line, the resulting value of y should be 5. 

Solving Simultaneous Linear Equations by using the Graphical Method

A linear graph is of the form y = mx + c, where m and c are constants. All linear graphs are straight lines, e.g. y = x, y = 2x - 1, etc. To draw a linear graph, you will only need two points. 

Given a pair of simultaneous linear equations, we can solve them algebraically as learnt earlier, or we can also use the graphical method to solve them. 
By plotting both graphs on the same axis, the answer can be found through finding the point(s) of intersection between the two graphs.

The following video is a worked example of how this can be done:

Number of solutions

A pair of simultaneous linear equations can have one solution, no solution or an infinite number of solutions.