Perpendicular lines question?

Question

8th grade Algebra 1.
Ok, here is the problem:

Write the equation of the line passing through the point and perpendicular to the given line.

(5,2) , y= -1/2x + 4

The answer in the book is y=2x-8

I don't understand how they got that answer and I don't get what to do. Help!!

Well if b= -8 , then plugging it in to
y= 2x + b would make the answer y= 2x-8, which is not what the book has.

Answer 1

Write the equation of the line passing through the point and perpendicular to the given line.

Point: (5,2)
Line: y = (-1/2)x + 4

The slope of the line perpendicular to the given line is the negative reciprocal.

m = -1/(-1/2) = 2

So the desired line is of the form:

y = 2x + b

Now plug in the given point and solve for b.

y = 2x + b
2 = 2*5 + b
2 = 10 + b
-8 = b

The equation of the perpendicular line is:

y = 2x - 8
_______

Please read your question again. First you said this is the answer in the book, then you said it wasn't. This really is the answer.

Answer 2

Plug in.

2 = 2(5) + B The slope is an opposite reciprocal because it's perpendicular

2 = 10+b
b= -8

so you use the opposite reciprocal for the slope

y = 2x + b and plug in b



y = 2x + 8