What is the equation of a line that is parallel to −x+3y=6 and passes through the point (3,5)?
what is the equation of a line that is perpendicular to −x+3y=9 and passes through the point (−3,2)?

What is the equation of a line that is parallel to −x+3y=6 and passes through the point (3,5)?

−x+3y=6
3y = x + 6 
y = 1/3x + 2 so slope m = 1/3

passes through the point (3,5)
y = mx + b
5 = 1/3(3) + b
5 = b or b = 5 
equation:
y = 1/3x +5

What is the equation of a line that is perpendicular to −x+3y=9 and passes through the point (−3,2)?
−x+3y=9
3y = x + 9
y = 1/3x + 3 so slope = 1/3
perpendicular slope = -3

passes through the point (−3,2)
y = mx + b
2 = -3(-3) + b
2 = 9 + b
-7 = b or  b = -7

equation
y = -3x - 7