A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b represents the y-intercept.
If the slopes of two lines are equal they are parallel, if one slope is minus the inverse of the other they are perpendicular, otherwise they are neither.
Comparing our lines to the slope-intercept form, we can find their slopes.
[tex]\begin{gathered} y=3x-7\Rightarrow m=3 \\ y=3x+1\Rightarrow m=3 \end{gathered}[/tex]Since their slopes are equal, those lines are parallel to each other.