SL 2.1—Equations of straight lines, parallel and perpendicular

A straight line can be written in several equivalent forms, each highlighting different features of the line. Knowing when to use each form is a key skill in IB Maths AA.

Gradient-Intercept Form: $y=mx+c$
where $m$ is the gradient and $c$ is the $y$-intercept. This is the most commonly used form and makes it easy to read off the gradient and $y$-intercept directly.

General Form: $ax+by+d=0$
where $a$, $b$, and $d$ are constants. (The letter $d$ is used here to avoid confusion with the $y$-intercept $c$ in gradient-intercept form.) The gradient is $-\frac{a}{b}$ and the $y$-intercept is $-\frac{d}{b}$.

Point-Gradient Form: $y-y_1=m(x-x_1)$
where $(x_1,y_1)$ is any known point on the line and $m$ is the gradient. This form is extremely useful when you are given a point and a gradient but do not know the $y$-intercept.