Equations of a Line

SL Core 2.1

A straight line is defined by its gradient and its y-intercept. The gradient-intercept equation of a line is thus:

y=mx+c📖

SL Core 2.1

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:

y−y1=m(x−x1)📖

SL Core 2.1

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

x=k

for some constant k.

SL Core 2.1

A horizontal line has gradient m=0. It is therefore in the form

y=c

for some constant c.

SL Core 2.1

The equation of a straight line can also be given in the form

ax+by+d=0📖

This reduces to

y=−bax−bd

In examinations, you may be asked to write the equation of a line in standard form.

Exercises