equation of a line when two points are given

We can clearly see a line ‘a’ whose equation is ax+by=c and which passes through two given points A and B. (x1,y1 ) are co-ordinates of A and (x2, y2 ) are co-ordinates of B. We can change the values of x1, y1, x2 and y2 using their corresponding slide bars. Observe how the position of the line changes as we change the values of x1, y1, x2 and y2.
Questions to think about Angle α between the line and the positive x-axis is given. Calculate tan⁡α, what you observe. Hint, compare tan⁡α with(y_2-y_1)/(x_2-x_1 ). What is the relation between (y_2-y_1)/(x_2-x_1 ) and slope of a line i.e. ‘m’? Fix point A (i.e. values of x1 and y1) and then move point B. What do you observe? Fix point B (i.e. values of x2 and y2) and then move the point A. What do you observe? We have the below equation for a straight line; (y-y_1 )=(y_2-y_1)/(x_2-x_1 ) (x-x_1 ) Now compare this with the given equation of ‘a’.