BestMaths

Gradients

A Reminder

A 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.

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.		m₁ = m₂
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