Writing equation in slope-intecept form

Question

Write the equation of the line, in slope-intercept form, perpendicular to 2x +3y = 8 and passing through the point (-3,1)

Answer 1

2x+3y = 8

3y = -2x +8

y = -2x/3 + 8/3

perpendicular has a negative inverse slope = 3/2

y =3x/2 + b, plug the point in, x=-3, y=1

1 = 3(-3)/2 +b

b =1+9/2 = 11/2

the equation of the perpendicular line is

y= 3x/2 + 11/2 with slope = 3/2 and intercept = 11/2