perpendicular equation?

Question

Write the standard form of the equation of the line that is perpendicular to y=2x-3 and passes throught (4,2)

the answer is x+2y-8=0
but how do i get that????

Answer 1

Take the negative reciprocal of the slope to make it the perpendicular.
y = -1/2x - 3

Change that into standard form.

Edit (9:26 PM):
original slope: 2
perpendicular of that slope: -1/2

*in finding the perpendicular line of a specific line, all you need to do is take the slope and take the negative reciprocal of it.

example (a):
equation: y = 3x + 5
perpendicular line: y = -1/3 +5

example (b):
equation: y = -5x - 1
perpendicular line: y = 1/5 - 1
**because -(-1/5) = 1/5

Answer 2

The line perpendicular to ax + by + c = 0 is of the form bx - ay + k = 0 where is an unknown constant. Substitute the given point in this equation(x + 2y + k = 0). u get k. substitute in the equation u get the answer as x + 2y - 8 = 0!

Answer 3

y=mx+b
2=-.5(4)+b
2=-2+b
b=4
y=-.5x+4
y=-.5x(-2)+4(-2)
=x+2y-8