Parallel equations have the same slope. First, let's identify the slope of the given equation, which is in the slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Comparing the given equation with this form, we have m = 3, so the slope is 3.
Now, let's identify the slope of each option:
[tex]\begin{gathered} x+y=18\\ \\ y=-x+18\\ \\ m=-1 \end{gathered}[/tex][tex]\begin{gathered} x-3y=-12\\ \\ 3y=x+12\\ \\ y=\frac{1}{3}x+4\\ \\ m=\frac{1}{3} \end{gathered}[/tex][tex]\begin{gathered} 3x+y=6\\ \\ y=-3x+6\\ \\ m=-3 \end{gathered}[/tex][tex]\begin{gathered} y-3x=7\\ \\ y=3x+7\\ \\ m=3 \end{gathered}[/tex]
Therefore the correct option is the fourth one: y - 3x = 7.
