[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's use slope - point form of line to get the required equation ~
[tex]\qquad \sf \dashrightarrow \:y - y_1 = m(x - x_1)[/tex]
where,
- m = slope of the line ( given in question )
- [tex] \sf{y_1 = 6} [/tex]
- [tex] \sf{x_1 = 9} [/tex]
Now, let's put in the values ~
[tex]\qquad \sf \dashrightarrow \:y - 6= \dfrac{5}{9} (x - 9)[/tex]
[tex]\qquad \sf \dashrightarrow \: y - 6 = \dfrac{5}{9} x - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: y = \dfrac{5}{9} x - 5 + 6[/tex]
[tex]\qquad \sf \dashrightarrow \: y = \dfrac{5}{9} x + 1[/tex]
So, the correct choice is A
