The equation of a line when two point 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. \(x_1, y_1)\)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’.