What is the equation of a line that is perpendicular to the line y = 2x + 4 and passes through the point (–2, 3)? A. y = –12x + 2
B. y = 2x + 2
C. y = –12x + 4
D. y = 2x + 4

3=-1/2(-2)+b

solve

3=1+b

2=b

b=2

now that we have the slope and y intercept of the equation construct your equation:

y=-1/2x+2

Neither of these answers are correct. I graphed them all and not a single one passed through (-2, 3)

Additionally, the slopes of B and D are inncorrect and lines A and C dont pass through the point (-2, 3) the only correct  equation is y=-1/2x+2

I graphed it and it was valid

Maybe ask your teacher if there were any mistakes?

Step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12