Equation of a line when a point n slope are given

Author:
Mathguru
We can clearly see a line ‘a’ whose equation is y=mx +c. We can change the values of m (slope of this line) and \(x_1, y_1)\), the co-ordinates of the given point A through which this line passes using their corresponding slide bars. Observe how the position of this line changes as we change the values of m, \(x_1\) and \(y_1\).
1. Angle α between the line and the positive x-axis is given. Calculate \(tan\alpha \) , what do we observe? Hint, compare \(tan\alpha \) with m. 2. Fix the values of\(x_1\) and \(y_1\) and change the value of m, what do we observe? Fix the value of m and change the value of \(x_1\) and\(y_1\) using their corresponding slide bars or by directly moving the point A, what do we observe? 3. Input values of\(x_1\) and\(y_1\) in the equation \(y - y_1 = m (x - x_1)\) and compare the result with equation of line ‘a’ which we see in the screen.