Question

Write a two point slope equations for the line passing through the points 6,5 and 3,1

Answer 1

Answer: The required equation is y= 4x/3 - 3

Step-by-step explanation:

Given points (6,5) and (3,1)

Two point slope equation is  given as

$y - y1 = \frac{y2-y1}{x2-x1}(x-x1)$

where (x1, y1) and (x2,y2) are the points respectively

∴ $y-5 =\frac{1-5}{3-6}(x-6)$

$y-5 =\frac{-4}{-3} (x- 6)$

$y -5 =\frac{4}{3} (x-6)$

$y - 5 =\frac{4}{3}x - 8$

$y = 5 +\frac{4}{3} x - 8$

$y = \frac{4}{3}x -3$

It can also be written as

$y -5 =\frac{4}{3}(x -6)$

Answer 2

The 2-point form of the equation of a line can be written as ...

... y = (y2-y1)/(x2-x1)·(x -x1) +y1

For your points, this is ...

... y = (1-5)/(3-6)·(x -6) +5

... y = (4/3)(x -6) +5

It can also be written as

... y -5 = (4/3)(x -6)