what is the equation of the line that is perpendicular to the line y=-1/2 (X -18) and intersects the Y axis at (0, -1)

The required equation of the line  is perpendicular line is 2x + y +1 = 0

Given ,

The equation of the line is Y =

We have to find ,

The equation of line which perpendicular to and intersects the Y-axis at (0, -1).

According to the question,

2Y = -1 ( X - 18)

2Y = -X + 18

2Y + x - 18 = 0

Then , the given line is perpendicular to the line to line

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 is perpendicular line is 2x + y +1 = 0 .

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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

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step-by-step explanation:

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