Respuesta :
Answer:
The line on which the east edge could be located is:
A) [tex]2x-y =96[/tex]
Step-by-step explanation:
The complete question is:
Amy is helping 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?
A) 2x − y = 96
B) −2x − y = 96
C) −y − 2x = 48
D) y + 2x = 48
Solution:
Given:
The east edge cannot intersect the west edge.
When two lines cannot meet each other, the lines are said to be parallel.
For two parallel lines the slope are same.
From the equation of line of west edge which is
[tex]y=2x+5[/tex]
we can tell the slope of line = 2 as the equation is in slope-intercept form of a straight line which is given as:
[tex]y=mx+b[/tex]
where [tex]m[/tex] represents slope and [tex]b[/tex] represents y-intercept.
Thus slope of east edge must be=2
In order to find the equation of line of east edge, we will represent each equation given in slope-intercept form and thus compare the slopes.
For a line to be a line of east edge, it must have slope =2
A) [tex]2x-y =96[/tex]
Adding [tex]y[/tex] both sides.
[tex]2x-y+y =96+y[/tex]
[tex]2x =96+y[/tex]
Subtracting both sides by 96.
[tex]2x-96 =96+y-96[/tex]
[tex]2x-96 =y[/tex]
The slope intercept form of equation is
[tex]y=2x-96[/tex]
So, slope of line = 2. Thus it is a possible equation of east edge.
B) [tex]-2x-y =96[/tex]
Adding [tex]y[/tex] both sides.
[tex]-2x-y+y =96+y[/tex]
[tex]-2x =96+y[/tex]
Subtracting both sides by 96.
[tex]-2x-96 =96+y-96[/tex]
[tex]-2x-96 =y[/tex]
The slope intercept form of equation is
[tex]y=-2x-96[/tex]
So, slope of line =-2. Thus it cannot be a possible equation of east edge.
C) [tex]-y-2x =48[/tex]
Adding [tex]y[/tex] both sides.
[tex]-y+y-2x=48+y[/tex]
[tex]-2x =48+y[/tex]
Subtracting both sides by 48.
[tex]-2x-48 =48+y-48[/tex]
[tex]-2x-48 =y[/tex]
The slope intercept form of equation is
[tex]y=-2x-48[/tex]
So, slope of line =-2. Thus it cannot be a possible equation of east edge.
D) [tex]y+2x =48[/tex]
Subtracting [tex]2x[/tex] both sides.
[tex]y+2x-2x=48-2x[/tex]
[tex]y =48-2x[/tex]
The slope intercept form of equation is
[tex]y=-2x+48[/tex]
So, slope of line =-2. Thus it cannot be a possible equation of east edge.
