Respuesta :
Answer:
The equation of the perpendicular line is 2 x + y + 1 =0
Step-by-step explanation:
Step(i) :-
Given equation of the line 2y = x - 18
x - 2y - 18 =0
The equation of the perpendicular line to the given line
b x - ay +k=0
-2 x - y + k =0 this line is passing through the point ( 0 , -1)
⇒ 0 -(-1) + k=0
⇒ 1+k =0
⇒ k = -1
Step(ii):-
The equation of the line is perpendicular to the line
-2x - y - 1 =0
2 x + y + 1 =0
Conclusion:-
The equation of the perpendicular line to the given line 2 x + y + 1 =0
The required equation of the line [tex]l_1[/tex] is perpendicular line [tex]l_2[/tex] is 2x + y +1 = 0
Given ,
The equation of the line [tex]l_1[/tex] is Y = [tex]-\frac{1}{2} ( X- 18 )[/tex]
We have to find ,
The equation of line which perpendicular to [tex]l_1[/tex] and intersects the Y-axis at (0, -1).
According to the question,
[tex]Y = \frac{-1}{2} (X - 18)[/tex]
2Y = -1 ( X - 18)
2Y = -X + 18
2Y + x - 18 = 0
Then , the given line is perpendicular to the line [tex]l_1[/tex] to line [tex]l_2[/tex]
b = 2 , a = 1 ,
bx - ay + k = 0
2x - 1y + k = 0
The intersection point the Y- axis ( 0 , -1 )
2(0) - 1(-1) + k = 0
0 + 1 + k = 0
k = -1
Put the value of k in equation and write the equation at Y - axis
-2x -y -1 = 0
The required line is 2x+y+1 = 0
The required equation of the line [tex]l_2[/tex] is perpendicular line [tex]l_1[/tex] is 2x + y +1 = 0 .
For the more information about Equation of the line click the link given below.
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