Answer:
Parallel line A : [tex]y=\frac{1}{4}x+1[/tex]
Perpendicular to line A : [tex]y=-4x-3[/tex]
Neither parallel nor perpendicular to line A : [tex]y=4x-8[/tex]
Step-by-step explanation:
The equation of line A is
[tex]y=\frac{1}{4}x+8[/tex] ... (1)
The slope intercept form of a line is
[tex]y=mx+b[/tex] .... (2)
where, m is slope and b is y-intercept.
From (1) and (2) we get
[tex]m=\frac{1}{4}[/tex]
It means the slope of line A is 1/4.
The slope of parallel lines are same and the product of slopes of two perpendicular lines is -1.
In equation [tex]y=\frac{1}{4}x+1[/tex], the slope is 1/4 which is same as slope of line A. So, line [tex]y=\frac{1}{4}x+1[/tex] is parallel to line A.
In equation [tex]y=4x-8[/tex], the slope is 4 which not equal to slope of line A and [tex]4\times \frac{1}{4}=1\neq -1[/tex]. So, line [tex]y=4x-8[/tex] is neither parallel nor perpendicular to line A.
In equation [tex]y=-4x-3[/tex], the slope is -4 which is not equal to the slope of line A and [tex]-4\times \frac{1}{4}=-1[/tex]. So, line [tex]y=-4x-3[/tex] perpendicular to line A.
