Equations of a Line
Gradient-intercept form, point-gradient form, vertical lines, horizontal lines, standard form of a line
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Gradient-intercept form
A straight line is defined by its gradient and its y-intercept. The gradient-intercept equation of a line is thus:
Point-gradient form
If we know a point (x1,y1) on a line and the gradient m of the line, we can use the point-gradient form of the line:
Vertical lines
A vertical line does not have a well defined gradient, since there is no "run" - the x-values never change.
We cannot write the equation of a vertical line in the form y=⋯. Instead we write
for some constant k.
Horizontal lines
A horizontal line has gradient m=0. It is therefore in the form
for some constant c.
Standard form of a line
The equation of a straight line can also be given in the form
This reduces to
In examinations, you may be asked to write the equation of a line in standard form.
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