If the line is parallel to
[tex]y=\frac{1}{3}x+4[/tex]Then it has a slope of 1/3.
Using this slope, point (-3, 5) and the slope-point form,
[tex]\begin{gathered} y-5=\frac{1}{3}(x+3) \\ \rightarrow y-5=\frac{1}{3}x+1 \end{gathered}[/tex]Clearing y to get the slope-intercept form,
[tex]\begin{gathered} y-5=\frac{1}{3}x+1 \\ \rightarrow y=\frac{1}{3}x+6 \end{gathered}[/tex]We get that the equation of the line in slope-intercept form is:
[tex]y=\frac{1}{3}x+6[/tex]