The ordered pairs in the table below represent a linear function.
What is the slope of the function?
1/4
1/2
2
4

The answer to your question is slope = 2

Step-by-step explanation:

Data

Point 1 = (6, 2)

Point 2 = (9, 8)

Process

1.- Write the formula to calculate the slope

       slope = m = (y2 - y1) / (x2 - x1)

2.- Identify the values of x1, y1, x2 and y2

       x1 = 6   y1 = 2   x2 = 9  y2 = 8

3.- Substitution

                    m = (8 - 2) / (9 - 6)

4.- Simplification

                    m = 6 / 3

5.- Result

                    m = 2

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