One of the most useful forms of the equation of a flat surface isWe have to be able to write the equations of lines in this form. We may have to do this in various ways.

We are given two points:
Find the line which passes throughand
The gradient of the line is

We are told a point on the line and the gradient of the line.
Find the equation of the line with gradient 5 which passes through (6,7).

We are told two perpendicular lines meet at a given point or a given value ofGiven the equation of one of the lines, find the equation of the other line.
A line meets the lineat right angles at the point P whose– coordinate is 2. Find the equation of the first line.
The y – coordinate ofis
The gradient of the line is 2 so the gradient of the perpendicular line is

We are told a line is parallel to some given line and passes through some point.
The line l is parallel toand passes throughFind the equation of
Since the lines are parallel the gradient