GCSE revision notes

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 x-coordinates. 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 x-coordinates. 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 straight-line.

A concise summary of gradients

So,

Example 1:

So, for example represents a straight line with a gradient of 2 and a y-intercept of 3.

The gradient of 2 means that for every 1 square across you go up 2 squares.

The y-intercept means it passes through 3 on the y-axis

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 y-intercept is -1 because it crosses through -1 on the y-axis

The equation is therefore

Example 2:

The gradient above is -2 because it goes across 1 and down 2

The y-intercept is +1 because it goes through +1 on the y-axis

The equation is therefore

Example 3:

A more difficult gradient

This line goes across 4 up 3.

The y-intercept 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

Re-arranging equations – a grade A* idea