Line mn passes through points m(4, 3) and n(7, 12). if the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

b = -9

Step-by-step explanation:

As we go from M(4, 3) to N(7, 12), x increases by 3 and y increases by 9.  Thus, the slope of the line segment connecting these two points is m = rise / run = m = 9/3, or just m = 3.

Subbing the coordinates of M into y = mx + b, we get:

3 = 3(4) + b, or 3 = 12 + b, so that b = -9.

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

good job you smart son of a gun you are smarter that einstein. 7