Equation of a line:

y = mx + b

what you know:

x₁,y₁
x₂,y₂

Therefore:

y₁ = mx₁ + b

y₂ = mx₂ + b

Subtracting:

y₁ - y₂ = m(x₁ - x₂)

if x₁ == x₂ then it is a vertical line on y

therefore (assuming x₁ != x₂)

m = (y₁ - y₂)/(x₁ - x₂)

substituting in first equation:

y₁ = (y₁ - y₂)/(x₁ - x₂)x₁ + b

b = y₁ - (y₁ - y₂)/(x₁ - x₂)x₁

therefore the equation of a line (assuming x₁ != x₂) is:

y = (y₁ - y₂)/(x₁ - x₂)x + (y₁ + y₁ - y₂)/(x₁ - x₂)x₁