slope = [tex]\frac{1}{6}[/tex]
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange x - 6y + 12 = 0 ( subtract x + 12 from both sides )
- 6y = - x - 12 ( divide all terms by - 6 )
y = [tex]\frac{1}{6}[/tex] x + 2 ← in slope-intercept form
with slope m = [tex]\frac{1}{6}[/tex]