How to find the equation of a line from two points?
Two-point form is used to find the equation of a line passing through two points. Its formula is given by,
y – y1 = m (x – x1)
or
[Tex]y – y_1 = \frac{y_2-y_1}{x_2-x_1}(x – x_1)[/Tex]
where,
m is the slope of line,
(x1, y1) and (x2, y2) are the two points through which line passes,
(x, y) is an arbitrary point on the line.
Derivation
Consider a line with two fixed points B (x1, y1) and C (x2, y2). Another point A (x, y) is an arbitrary point on the line.
As the points A, B and C are concurrent the slope of AC must be equal to BC.
Using the formula for slope we get,
(y – y1) / (x – x1) = (y2 – y1) / (x2 – x1)
Multiplying both sides by (x – x1) we get,
[Tex]y – y_1 = \frac{y_2-y_1}{x_2-x_1}(x – x_1)[/Tex]
This derives the formula for two point form of a line.