Every straight line can be represented algebraically in the form y = mx + c , where
m = represents the gradient of a line (its slope, steepness)
c = represents the y intercept (a point where the line crosses the y axis)
Furthermore, there are several ways in which you can describe a straight line algebraically
Equation of a line=

Line gradient m , the intercept on y axis is c
,

Line gradient m , passes through the origin

,

Line gradient 1, makes an angle of 45 0 with the x axis, and the intercept on the y axis is c

,

Line is parallel to the x axis, through (0, k)


Line is the x axis

.

Line is parallel to the y axis, through ( k , 0)

,

Line is the y axis


, General form of the equation of straight line

The gradient measures the steepness of the line.
It is defined as
, or
When the gradient is 1, the line makes a 45 0 angle with either axes. If the gradient is 0, the line is parallel to the x axis.

Equation of a straight line given the gradient and a point=
On the coordinate plane, the slant of a line is called the slope. Slope is the ratio of the change in the yvalue over the change in the xvalue, also called rise over run.
Given any two points on a line, you can calculate the slope of the line by using this formula:
slope =
f the point is given by its coordinates
, and the gradient of a line is given as
m , you can deduce the equation of that line.
You are using the formula for gradient,
, to derive a formula for the line itself. The coordinates of the point can be substituted, while the
y 2 and
x 2 need to remain (without the superscript numbers).
Then simply substitute the given values into
The equation of a line given two points=
When you have this kind of problem, you take that, as both points belong to the same line, the gradients at both points will be the same.
It makes sense therefore to say that
All you need to do in this case will be to substitute coordinates you have for the given points
and
.
Parallel and perpendicular lines
When two lines are parallel, their gradient is the same:
When two lines are perpendicular, their product equals 1:
.
The line length
The length of the line segment joining two points will relate to their coordinates. Have a good look at the diagram
The length joining the point A and C can be found by using Pythagoras' Theorem:
Midpoint of a line
Midpoint of the line can be found by using the same principle
So the point between A and C will have the coordinates
If you know the midpoint, you can easily find the perpendicular bisector of a given line. This new line will go through the midpoint of the given line, and it will be perpendicular to it.
Pairs of Straight Lines
Any two lines through the Origin may be written as and where and are their gradients. So giving or must represent the pair.
The general form of this equation is given by:
This equation must represent a pair of straight lines, real or imaginary, through the origin. These can be written as