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IB Math AAHL

Cartesian plane & lines

Equations of a Line

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Equations of a Line - Exercises | IB Math AAHL | Perplex

Equations of a Line

Gradient-intercept form, point-gradient form, vertical lines, horizontal lines, standard form of a line

Want a deeper conceptual understanding? Try our interactive lesson!

Exercises

No exercises available for this concept.

Key Skills

Gradient-intercept form

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📖

Point-gradient form

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)📖

Vertical lines

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.

Horizontal lines

SL Core 2.1

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

y=c

for some constant c.

Standard form of a line

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.

Gradient-intercept form

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📖

Point-gradient form

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)📖

Vertical lines

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.

Horizontal lines

SL Core 2.1

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

y=c

for some constant c.

Standard form of a line

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.