# The equation of a line when two point are given.

Author:
Mathguru
We can clearly see a line ‘a’ whose equation is $$ax+by = c$$and which passes through two given points A and B. $$x_1, y_1)$$are co-ordinates of A and $$x_2, y_2)$$are co-ordinates of B. We can change the values of $$x_1$$, $$y_1$$, $$x_2$$ and $$y_2$$ using their corresponding slide bars. Observe how the position of the line changes as we change the values of $$x_1$$, $$y_1$$, $$x_2$$ and $$y_2$$.
Questions to think about 1. Angle α between the line and the positive x-axis is given. Calculate $$tan\alpha$$ , what you observe. Hint, compare $$tan\alpha$$ with $$\frac{y_2 - y_1}{x_2- x_1}$$ 2. What is the relation between $$\frac{y_2 - y_1}{x_2- x_1}$$and slope of a line i.e. ‘m’? 3. Fix point A (i.e. values of $$x_1$$ and $$y_1$$) and then move point B. What do you observe? 4. Fix point B (i.e. values of $$x_2$$ and $$y_2$$) and then move the point A. What do you observe? 5. We have the below equation for a straight line; $$y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}\left ( x - x_1 \right )$$ Now compare this with the given equation of ‘a’.