\frac{y_{_A}-y_{_B}}{x_{_A}-x_{_B}}=m

1

2

P = (x ; y)

P(x;y)

\frac{y-y_{_A}}{x-x_{_A}}=m

3

4

\frac{y-y_{_B}}{x-x_{_B}}=m

5

6

7

A = (2, 2)
B = (8, -1)
a = Line(A, B)
P = Point(a)
i = (1, 0)
j = (0, 1)
texto2: "\frac{" + (LaTeX[(A * j)]) + "-" + LaTeX[(B * j)] + "}{" + LaTeX[(A * i)] + "-" + LaTeX[(B * i)] + "}=\frac{" + LaTeX[(A * j) - (B * j)] + "}{" + LaTeX[(A * i) - (B * i)] + "}=" + LaTeX[((A * j) - (B * j)) / ((A * i) - (B * i))] + ""
b = false
c = false
d = false
texto5: "\frac{ " + (LaTeX[(P * j)]) + "-" + LaTeX[(A * j)] + " }{ " + LaTeX[(P * i)] + "-" + LaTeX[(A * i)] + " }=\frac{ " + LaTeX[(P * j) - (A * j)] + "}{ " + LaTeX[(P * i) - (A * i)] + "}=" + LaTeX[((P * j) - (A * j)) / ((P * i) - (A * i))] + ""
e = false
f = false
texto7: "\frac{ " + (LaTeX[(P * j)]) + " - " + LaTeX[(B * j)] + " }{  " + LaTeX[(P * i)] + "-  " + LaTeX[(B * i)] + "}=\frac{ " + LaTeX[(P * j) - (B * j)] + " }{ " + LaTeX[(P * i) - (B * i)] + " }= " + LaTeX[((P * j) - (B * j)) / ((P * i) - (B * i))] + ""
g = false
h = false
C = (3, 5)
D = (6, 2)
k = Line(C, D)
texto8: "\frac{y_{_C}-y_{_D}}{x_{_C}-x_{_D}}=\frac{" + (LaTeX[(C * j)]) + "-" + LaTeX[(D * j)] + "}{" + LaTeX[(C * i)] + "-" + LaTeX[(D * i)] + "}=\frac{" + LaTeX[(C * j) - (D * j)] + "}{" + LaTeX[(C * i) - (D * i)] + "}=" + LaTeX[((C * j) - (D * j)) / ((C * i) - (D * i))] + "=m_2"
l = false
m = false