Definitions
A Reminder
 A Cartesian graph is a graph drawn on a number plane with two perpendicular axes, the xaxis and the yaxis.
 Coordinates are the ordered pairs that locate points on a graph. The first number is the distance along the xaxis (horizontal) and the second number is the distance along the yaxis (vertical).
 Each point is located by an ordered pair. e.g. (x, y), (3, 4)
 The origin is the point where the two axes intersect. The origin has coordinates of (0, 0).
 The intercepts of a graph are the points where the graph cuts the xaxis and yaxis.
Gradient
The gradient of a straight line is a measure of its slope.
The gradient, m is defined as:
Gradients can be given as integers, fractions or decimals.
Types of gradient
A line sloping upwards from left to right has a positive gradient.


m is positive

A line sloping downwards from left to right has a negative gradient.


m is negative

Parallel lines have the same gradient.


m_{1} = m_{2}

A horizontal line has a gradient of 0.


m = 0

The gradient of a vertical line is undefined.


m is undefined

Click Here for practice at calculating gradients.
Example

Answer

What is the gradient of the line below?


What is the gradient of the line joining the points P (1, 2) to Q (4, 5)? 
Draw a diagram

What is the gradient of the line joining the points M (2, 3) to N (3, 5)? 
Draw a diagram

