Find an equation of a line parallel to y=-3x +4 that goes through the point (-2,5).

y=-3x-1

Step-by-step explanation:

Parallel lines have the same slope. Since the original line has a slope of -3, the line that is parallel to it also has a slope of -3.

1. Use point-slope: y-y1=m(x-x1). M represents slope and x1 and y1 represent the x and y values of the ordered pair.

y-5=-3(x+2)

2. Simplify

First, distribute -3 to x and +2

Rewrite the equation as y-5=-3x-6

Add 5 to both sides

y=-3x-1

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step-by-step explanation:

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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