Amy is helping plan her school's new basketball court. The west edge of the basketball court is located on the line $$ y=-4 x $$. The east edge cannot intersect with the west edge. On which line could the east edge be located? $$ \begin{array}{l}y-4 x=-200 \ -4 x-y=-50 \ 4 x-y=-200 \ -y+4 x=-50\end{array} $$ \begin{tabular}{l} \ \hline\end{tabular}

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UpStudy AI · Accepted Answer

The west edge is on the line 
$$
y = -4x,
$$
so its slope is $$-4$$. For the east edge not to intersect the west edge, it must be parallel to the west edge, meaning its slope must also be $$-4$$.

We check the given options:

1. For the line $$y - 4x = -200$$, rewriting gives:
   $$
   y = 4x - 200,
   $$
   which has a slope of $$4$$. This is not parallel.

2. For the line $$-4x - y = -50$$, rewriting gives:
   $$
   -y = 4x - 50 \quad \Rightarrow \quad y = -4x + 50.
   $$
   This line has a slope of $$-4$$. It is parallel, and since the constant is different, it does not coincide with the west edge.

3. For the line $$4x - y = -200$$, rewriting gives:
   $$
   -y = -4x - 200 \quad \Rightarrow \quad y = 4x + 200,
   $$
   which has a slope of $$4$$.

4. For the line $$-y + 4x = -50$$, rewriting gives:
   $$
   -y = -4x - 50 \quad \Rightarrow \quad y = 4x + 50,
   $$
   which also has a slope of $$4$$.

Thus, the line that could be the east edge is:
$$
-4x - y = -50.
$$
The east edge can be on the line $$ -4x - y = -50 $$.

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