Recall that two lines are parallel if they have the same slope.
Now, the given equation is in the form
[tex]y=mx+b,[/tex]where m is the slope. Therefore, the slope of the given line is
[tex]\frac{1}{3},[/tex]and it has to be the slope of the parallel line.
Taking the options to their slope-intercept form, we can determine which equation represents a parallel line to the given line.
Answer: An equation of the form:
[tex]y=\frac{1}{3}x+b\text{.}[/tex]Where b is a constant.
