Introduction to Linear Equations

A straight line can be described algebraically in several equivalent forms. Each form highlights different features of the line, and being able to move fluently between them is a core skill in IB Math AI SL.

Linear Equation

An equation whose graph is a straight line. It contains no powers of variables higher than 1.

The three main forms you need to know are:

Gradient-Intercept Form: $y = m x + c$
General Form: $a x + b y + d = 0$
Point-Gradient Form: $y - y_{1} = m (x - x_{1})$

All three forms describe the same line — they are simply different ways of writing the same relationship.

Exam Tip

In an exam, always check which form the question asks you to give your final answer in. If it says "in the form $a x + b y + d = 0$ ", make sure you rearrange fully and that $a$ , $b$ , and $d$ are integers.

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SL 2.1—Equations of a line

Introduction to Linear Equations

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