Equations from Intercepts — Cheat sheet

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Intercept form

$\dfrac{x}{a} + \dfrac{y}{b} = 1$ - where $a$ is the $x$ -intercept and $b$ the $y$ -intercept.

Situation	Move
Intercepts to equation	substitute into intercept form, clear denominators
Equation to $x$ -intercept	set $y = 0$ and solve
Equation to $y$ -intercept	set $x = 0$ and solve
Slope from intercepts	$m = -\dfrac{b}{a}$

Line	Why
Through the origin	both intercepts are $0$ , denominators vanish
Horizontal $y = c$	no $x$ -intercept
Vertical $x = c$	no $y$ -intercept