Question

What is an equation in point-slope form for the line perpendicular to y = 2x + 13 that contains (8,-4)?

Select one:
O a. y + 4 = -1/2(x-8)

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

O c. y + 4 = 2(x - 8)

O d. y+ 8 = -1/2(x-4)

Answer 1

Y = -½x

OR

y+4= -½(x-8)

Explanation:

For perpendicular lines ,L1 and L2 ,the following relation hold;

Gradient of L1 × Gradient of L2= -1

i.e

Product of their gradients equal to one for perpendicular lines

GL1.GL2 =-1

from equation given

y=2x+ 13

it is in the form y =mx +c,where

m is the gradient and c is constant.

therefore the gradient of the line is

2, since 2 is in position of m

=> GL1 = 2

2 GL2 = -1

=> GL2 =-½

Since gradient is given by =

( change in y)/(change in X)

(y+4)/(x-8)=-½

=> -½x+4=y+4

=> y=-½x

therefore the equation is

y=-½x