Question

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

Answer 1

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)

Answer 2

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

Explanation:

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

Two point slope equation is given as

`y - y1 = (y2-y1)/(x2-x1)(x-x1)`

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

∴
`y-5 =(1-5)/(3-6)(x-6)`

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

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

`y - 5 =(4)/(3)x - 8`

`y = 5 +(4)/(3) x - 8`

`y = (4)/(3)x -3`

It can also be written as

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