Write an equation of the line that passes through the given two points
A two-point form of the equation is used when two different points on the line are known.
Answer: The general equation of the line is y - y1 = [(y2 - y1) / (x2 - x1)] (x - x1)
This equation can easily be simplified to any of the forms of the equation like the slope-intercept form, so as to calculate the intercept value by comparison.
Let the given points are (x1, y1) and (x2, y2)
Therefore, applying the slope-intercept form of the equation,
⇒ y - y1 = m (x - x1)
⇒ m = slope = (y2 - y1) / (x2 - x1)
Consider an example.
Let the two given points be (1, 0) and (3, 4)
Slope of the line
= (4 - 0) / (3 - 1 )
= 4 / 2 = 2 ------------ (1)
Using the point (1, 0), let's write the equation of the line
Using the general form of the equation i.e. y - y1 = [(y2 - y1) / (x2 - x1)] (x - x1)
(y - 0) = m (x - 1) [Since, (y2 - y1) / (x2 - x1) = m]
⇒ y = 2(x - 1) [From (1), m = 2]
⇒ y = 2x - 2