Take the point (6,9)

hence you have asked me find an equqtion that is pallrallel to the line whose inclination is arctan 2

it should be,

y-9=2*x-6

y-9=2x-12

y=2x-3

nextly, take the (7,-3)

hence you asked me an equation of line which is pendecular to the inclination is arctan 2/3

these implies

that the inclination of line is to be

inclination is arctan ‘-3/2’

i.e.,

-1/2/3,implies that -3/2

above one is can be study as -1 whole divided 2 divided by 3

now your second equation is,

y+3=-3/2*x-7

2*y+3=-3x+21

2y+6=-3x+21

2y=-3x+15

y=-3/2*x+15/2

hence required equation are

y=2x-3 &

y=-3/2*x+15/2

hence these answer should satisfy you up to some extent so that you can get an ideas,

Best of luck!!!!!!!!!!!!!!!!!!!!!!!!