How does one find the equation of a line passing through 2 points of a graph?

The general equation for a line on a graph is: y = mx + b ,where a is called the slope of the graph and b is the y-intercept(or the point where the line crosses the y axis). Let's assume the 2 points have the following coordinates (x₁ , y₁) and (x₂ , y₂). Subtracting the 2 equations from one another to get, y₁ -y₂ = mx₁ + b - mx₂ -b . The b's could be cancelled out and the m is a common multiplier , which means the equation could be written as:y₁-y₂ = m(x₁-x₂) or m = (y₁-y₂)/(x₁-x₂). Assuming we know all x's and y's m could be calculated. The final step of finding b could be done by substituting m and a pair of x and y into the first equation(y=mx+b)