For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the statement we have the following equation:
[tex]y = \frac {1} {3} x + 4[/tex]
Where:
[tex]m = \frac {1} {3}[/tex]
By definition, if two lines are parallel then their slopes are equal.
Thus, the second equation will be of the form:
[tex]y = \frac {1} {3} x + b[/tex]
We substitute the given point and find "b":
[tex]-5 = \frac {1} {3} (0) + b\\b = -5[/tex]
Finally, the equation is:
[tex]y = \frac {1} {3} x-5[/tex]
Answer:
Option D
