25 points write the equation for the following relation. include all of your work in your final answer. submit your solution. r = {(x, y): (2, 3), (4, 4), (6, 5), (8, 6), . .}

R = {(x, y): (4, 5), (8, 7), (12, 9), (16, 11), . . .}

Notice that y increases by 2 when x increases by 4

slope = 2/4 = 1/2

Notice that if you decrease x by 4 y will decrease by 2

So, y-intercept = (0,3)

Equation: y = (1/2)x+3

R = {(x, y): (2, 3), (4, 4), (6, 5), (8, 6), . . .}

slope = 1/2

y-int: (0,1)

Equation: y = (1/2)x + 1

Q = {(x, y): (2, 8), (3, 27), (4, 64), (5, 125), . . .}

Not a linear relation because y does not increase consistently

as x increases.

Equation: y = x^3

P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}

slope = 4

y-int: -4

Equation: y = 4x-4

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

g

step-by-step explanation: