Mr. Integral
Math notes/Pre-Calculus/Analytic Geometry

Writing Line Equations — Cheat sheet

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The one formula

y−y0=m(x−x0)y - y_0 = m(x - x_0) - slope mm, any known point (x0,y0)(x_0, y_0). Standard form: ax+by+c=0ax + by + c = 0. Slope-intercept: y=mx+ny = mx + n.

Finding $m$ first

GivenSlope
Two pointsm=y2−y1x2−x1m = \dfrac{y_2 - y_1}{x_2 - x_1}
Intercepts (p,0)(p,0), (0,q)(0,q)m=−qpm = -\dfrac{q}{p}
Inclination angle α\alpham=tan⁡αm = \tan\alpha
Through the origin and (a,b)(a,b)m=bam = \dfrac{b}{a}

Traps

Watch forNote
Line through the originconstant term is 00: the form is ax+by=0ax + by = 0
Obtuse inclinationtan⁡135∘=−1\tan 135^\circ = -1 - the line falls
tan⁡90∘\tan 90^\circundefined: vertical line x=x0x = x_0, no y=mx+ny = mx + n form
Choice of pointeither of two given points gives the same final equation