Straight Lines

Cartesian Notation

In Cartesian notation the position of a point is measured with respect to a reference point O, called the origin, and (in 2 dimensions) two perpendicular lines that pass through O.

e.g. A point P with coordinates (3,2) can be represented graphically by:

Straight Line

A Straight Line has the general form      
y = mx+c

m is the gradient of the line and is equal to the change in y (rise) divided by the change in x (step).

c is the point where the line meets the y-axis and is known as the “y-intercept”




To identify the intercept and the gradient of a straight line it needs to be put in the form 

y = mx + c

e.g. has gradient  m = 2  and the y-intercept, 
c = -1.  

A straight line may also be written in the form        

             ax+by+c=0   (where a, b and c are usually integers)

To find the gradient and y-intercept of lines in this form you need to manipulate the equation into the form               

                                 y = mx + c

eg

In general, to determine the equation of a straight line you need:

either

The gradient of the line and the coordinates of one point on the line

or

The coordinates of two points on the line

Equation of a line

The equation of the line through the point (x1 , y1) which has a gradient of m is found using:

e.g.  Find the equation of the line through the point (-2,4) with a gradient of 2

equation is                or

                       

             

The equation of the line through the points (x1 , y1) and (x2 , y2) is found using: