The perpendicular vector of 3x + y = -8 would be [3, 1]. Thus, you know that the slope would be 1/3 (the vector is in the form of [x, y]).
Use point-slope form with the perpendicular slope and the point (-3, 1):
[tex]y - y_1 = m(x-x_1)[/tex]
[tex]y - 1 = \frac{1}{3}(x + 3) [/tex]
You can simplify this if you want to (maybe to make it look a bit more "cleaner") and either put it as standard form or slope-intercept form.
