Answer:
b = 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x + y - 8 = 0 ( subtract 3x - 8 from both sides )
y = - 3x + 8 ← in slope- intercept form
with slope m = - 3
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= 
Consider the second line with equation
- 2x + by + 9 = 0 ← rearrange into slop- intercept form
by = 2x - 9 ( divide terms by b ( b ≠ 0 )
y =
x -
← in slope- intercept form
with slope m = 
Then
=
( cross- multiply )
b = 6