\vec{d}

\vec{OA}

\vec{OX}

Activa rastro de X

Desactiva rastro

Ver ecuación vectorial

Ver ecuaciones paramétricas

Ver forma continua

Ver ecuación general

Ver recta

He creado una herramienta para pintar la ecuación general 
pero fallaba para rectas horizontales y lo he parcheado con un texto 
llamado excepcion

Animación

B = (6, 2)
O = (0, 0)
d = Vector(O, B)
A = (1, 5)
t = 1.5 (slider from -5 to 10, step 0.01)
OA = Vector(O, A)
X: A + (t * d)
AX = Vector(A, X)
u = Vector(O, X)
texto5: "X = " + (LaTeX[A]) + " + t (" + (LaTeX[x(d)]) + "," + (LaTeX[y(d)]) + ")"
aa = false
xd = If(x(d) > 0, "+ " + (x(d)) + "t", If[x(d)  <  0, " " + (x(d)) + "t", ""])
yd = If(y(d) > 0, "+ " + (y(d)) + "  t", If[y(d)  <  0, " " + (y(d)) + "  t", ""])
yA = If(y(A) > 0, "- " + (y(A)), If[y(A)  <  0, "+ " + ((-y(A))), ""])
xA = If(x(A) > 0, "- " + (x(A)), If[x(A)  <  0, "+ " + ((-x(A))), ""])
texto7: "\frac{x" + (LaTeX[xA]) + "}{" + (LaTeX[x(d)]) + "} =\frac{y" + (LaTeX[yA]) + " }{ " + (LaTeX[y(d)]) + "}"
r = Line(A, d)
bb = false
cc = false
e = false
f = false
texto6: "x  = " + (LaTeX[x(A)]) + "" + (LaTeX[xd]) + " \\
y  = " + (LaTeX[y(A)]) + " " + (LaTeX[yd]) + "    "
coefs: {x(r), y(r), z(r)}
mcd = If(x(r) ≟ 0 ∨ (floor(x(r)) ≠ x(r)) ∨ (floor(y(r)) ≠ y(r)) ∨ (floor(z(r)) ≠ z(r)), x(r), (sgn(x(r)) * GCD[coefs]))
a: x(r) / mcd
b: y(r) / mcd
c: z(r) / mcd
tx = If(a ≟ 1, "x", a + " x")
ty = If(b ≟ 1, " + y", b ≟ -1, " - y", b ≟ 0, "", b > 0, " + " + b + " y", b  <  0, " - " + ((-b)) + " y")
tz = If(c ≟ 0, " = 0", c > 0, " + " + c + " = 0", " - " + ((-c)) + " = 0")
gene: "" + (tx + ty + tz) + ""
excepcion = If(y(A) ≟ 0, "y = 0", y(A)  <  0, "y + " + ((-y(A))) + " = 0", "y - " + (y(A)) + " = 0")
texto3: "" + (LaTeX[t]) + "  \space d"
texto8: "" + (LaTeX[tx + ty + tz]) + ""

Tool: EcGeneral
recta
Input: r
Output: gene

coefs: {x(r), y(r), z(r)}
mcd = If(x(r) ≟ 0 ∨ (floor(x(r)) ≠ x(r)) ∨ (floor(y(r)) ≠ y(r)) ∨ (floor(z(r)) ≠ z(r)), x(r), (sgn(x(r)) * GCD[coefs]))
a: x(r) / mcd
b: y(r) / mcd
c: z(r) / mcd
tx = If(a ≟ 1, "x", a + " x")
ty = If(b ≟ 1, " + y", b ≟ -1, " - y", b ≟ 0, "", b > 0, " + " + b + " y", b  <  0, " - " + ((-b)) + " y")
tz = If(c ≟ 0, " = 0", c > 0, " + " + c + " = 0", " - " + ((-c)) + " = 0")
gene: "" + (tx + ty + tz) + ""