### Definitions

A Reminder
• Cartesian graph is a graph drawn on a number plane with two perpendicular axes, the x-axis and the y-axis.
• Coordinates are the ordered pairs that locate points on a graph. The first number is the distance along the x-axis (horizontal) and the second number is the distance along the y-axis (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 x-axis and y-axis. 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.

 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. m1 = m2 A horizontal line has a gradient of 0. m = 0 The gradient of a vertical line is undefined. m is undefined

 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 