For the equation:
[tex]y=-\frac{1}{3}x-4[/tex]The slope is
[tex]m=-\frac{1}{3}[/tex]And the y-intercept is (0,-4)
Since the two lines does not have the same slope, they are not parallel.
Since the product of the slope of the two lines is not equal to -1, they are not perpendicular.
The slopes are neither equar nor opposite reciprocals.