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: 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
[tex]y - y1 = \frac{y2-y1}{x2-x1}(x-x1)[/tex]
where (x1, y1) and (x2,y2) are the points respectively
∴ [tex]y-5 =\frac{1-5}{3-6}(x-6)[/tex]
[tex]y-5 =\frac{-4}{-3} (x- 6)[/tex]
[tex]y -5 =\frac{4}{3} (x-6)[/tex]
[tex]y - 5 =\frac{4}{3}x - 8[/tex]
[tex]y = 5 +\frac{4}{3} x - 8[/tex]
[tex]y = \frac{4}{3}x -3[/tex]
It can also be written as
[tex]y -5 =\frac{4}{3}(x -6)[/tex]
