This section runs through the key points associated with the EQUATION OF A LINE
Make sure you understand EVERY ASPECT covered. It is a
source of particularly easy marks in the examination. DO NOT SKIP through any
section.
Key skill 1: The basic equation of a line – how to plot a line Suppose you are asked to draw the line with the equation Start by sketching the following table in which we choose
three xcoordinates. The simplest ones are
Now work out what the is for EACH of the by using the given equation When , When , When , We get the following table:
Now plot the coordinates, remembering the is the horizontal axis and the is the vertical axis AND DRAW A LINE THROUGH
THE POINTS

Key skill 2: Negatives in the equation Suppose you are asked to draw the line with the equation Again, start by sketching the following table in which we
choose three xcoordinates. The simplest ones are
Now work out what the is for EACH of the by using the given equation When , When , When , We get the following table:
Now plot the coordinates, remembering the is the horizontal axis and the is the vertical axis AND DRAW A LINE THROUGH
THE POINTS

Straight lines and
gradients
Any equation of the
form is always a straightline.
A concise summary
of gradients
So,












Example 1:
So, for example represents a straight line with a gradient of
2 and a yintercept of 3.
The gradient of 2 means that for every
1 square across you go up 2 squares.
The yintercept means it passes through 3
on the yaxis
Below are various examples of different gradients,
including some more difficult ones
Example 1:
The gradient above equals 3 since it goes across 1 and up 3.
The yintercept is 1 because it crosses through 1 on the yaxis
The equation is therefore
Example 2:
The gradient above is 2 because it goes across 1 and down 2
The yintercept is +1 because it goes through +1 on the yaxis
The equation is therefore
Example 3:
A more difficult gradient
This line goes across 4 up 3.
The yintercept is +1
Parallel lines
Parallel lines always have the same
gradient. These are examples of pairs of parallel lines
It doesn’t matter what you add or
subtract as long as the number before the x is the same
Perpendicular Gradients
To find a perpendicular gradient: he sign
changes and you find the “RECIPROCAL”
So, to find the equation of a line
perpendicular to
This lines has a gradient of
So the perpendicular line has a gradient
of
Rearranging
equations – a grade A* idea