To determine which line could be the location of the east edge of the basketball court, we need to ensure that it does not intersect with the line representing the west edge, which is given by [tex]\( y = -4x \)[/tex].
Let's analyze each of the given lines to see if they intersect with the line [tex]\( y = -4x \)[/tex].
1. Line 1: [tex]\( y - 4x = -200 \)[/tex]
Rewrite it in slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[
y - 4x = -200 \rightarrow y = 4x - 200
\][/tex]
The slope [tex]\( m \)[/tex] of this line is [tex]\( 4 \)[/tex], which is different from the slope of the west edge ([tex]\( -4 \)[/tex]). Therefore, this line will intersect with [tex]\( y = -4x \)[/tex].
2. Line 2: [tex]\( -4x - y = -50 \)[/tex]
Rewrite it in slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[
-4x - y = -50 \rightarrow -y = 4x - 50 \rightarrow y = -4x + 50
\][/tex]
The slope [tex]\( m \)[/tex] of this line is [tex]\( -4 \)[/tex], which is the same as the slope of the west edge ([tex]\( -4 \)[/tex]). Therefore, this line is parallel to [tex]\( y = -4x \)[/tex] and does not intersect with it.
3. Line 3: [tex]\( 4x - y = -200 \)[/tex]
Rewrite it in slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[
4x - y = -200 \rightarrow -y = -4x - 200 \rightarrow y = 4x + 200
\][/tex]
The slope [tex]\( m \)[/tex] of this line is [tex]\( 4 \)[/tex], which is different from the slope of the west edge ([tex]\( -4 \)[/tex]). Therefore, this line will intersect with [tex]\( y = -4x \)[/tex].
4. Line 4: [tex]\( -y + 4x = -50 \)[/tex]
Rewrite it in slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[
-y + 4x = -50 \rightarrow -y = -4x - 50 \rightarrow y = 4x + 50
\][/tex]
The slope [tex]\( m \)[/tex] of this line is [tex]\( 4 \)[/tex], which is different from the slope of the west edge ([tex]\( -4 \)[/tex]). Therefore, this line will intersect with [tex]\( y = -4x \)[/tex].
From this analysis, the only line that does not intersect with [tex]\( y = -4x \)[/tex] is the second line:
[tex]\[
-4x - y = -50 \quad \text{or} \quad y = -4x + 50
\][/tex]
Thus, the east edge of the basketball court could be located on the line
[tex]\[
\boxed{-4x - y = -50}
\][/tex]
