The general line equtaion passing through a point (x, y) is given by,
[tex]y=mx+b[/tex]
Here, m is the slope and b is the y intercept.
The given equation can be written as,
[tex]\begin{gathered} B\rightarrow y=2x+4 \\ N\rightarrow y=-\frac{x}{2}+4 \\ S\rightarrow y=2x-11 \end{gathered}[/tex]
From the above equtaions, the slope for each line can be calculated as,
[tex]\begin{gathered} B\rightarrow2 \\ N\rightarrow-\frac{1}{2} \\ S\rightarrow2 \end{gathered}[/tex]
For two lines to be perpendicular, the slopes are reciprocal two each other and in opposite sign.
From the above equations we can say that, N is perpendicuar to B and S. For two parallel lines, the slopes are equal. Therefore we can say, B and S are parallel to ecah other.
Therefore, for the trcaks to form a rectangle, the fourth line should be made perpendicular to B and S and in parallel eith N.
Therefore, the slope of the line is, -1/2. Hence the possible equaton can be,
[tex]y=-\frac{1}{2}x-11[/tex]
