Amy is plan her school's new basketball court. the west edge of the basketball court is located on the line y = 2x + 5. the east edge cannot intersect with the west edge. on which line could the east edge be located?
2x − y = 96
−2x − y = 96
−y − 2x = 48
y + 2x = 48

Line of east wedge is: 2x - y = 96

So, Option 1 is correct.

Step-by-step explanation:

The east edge cannot intersect with the west edge means that two lines are parallel.

If the two lines are parallel then they have same slope. We need to find the slopes of given lines and check which line has slope same as slope of west edge.

Slope of west edge.

y = 2x + 5

The standard equation for slope intercept form is:

y = mx+b

where m is the slope. So, m= 2

Now finding line for east edge.

Option 1.

Convert each given equation to standard slope intercept form and find the slope.

2x -y =96

-y = -2x +96

Multiply with -1

y = 2x -96

m = 2

Option 2.

-2x -y = 96

-y = 2x +96

y = -2x-96

m = -2

Option 3

-y-2x =48

-y = 2x +48

y = -2x -48

m = -2

Option 4.

y+2x = 48

y = -2x+48

m = -2

So, only line of Option 1 has slope = 2 which is equal to the slope of west edge.

Line of east wedge is: 2x - y = 96

So, Option 1 is correct.

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