The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of a line [tex]\dfrac{1}{3}x+y=-2[/tex]
Convert to the slope-intercept form:
[tex]\dfrac{1}{3}x+y=-2[/tex] subtract 1/3x from both sides
[tex]\boxed{y=-\dfrac{1}{3}x-2}\to\boxed{B.}[/tex]