Answer: [tex]y=\dfrac{1}{3}x+4[/tex]
Step-by-step explanation:
The equation of a line passing through (a,b) and (c,d) is given by :_
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
The given points : (3,5) and (9,6)
Then , the equation of a line passing through (3,5) and (9,6) will be :-
[tex]y-5=\dfrac{6-5}{9-3}(x-3)\\\\\Rightarrow\ y-5=\dfrac{1}{3}(x-3)\\\\\ y=\dfrac{1}{3}x-1+5\\\\\Rightarrow\ y=\dfrac{1}{3}x+4[/tex]
Hence, the equation of the line in slope -intercept form : [tex]y=\dfrac{1}{3}x+4[/tex]
