What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)? y = -3/2x+7/2 2y = -3x + 7 2x + 3y - 7 = 0

The equation of the line would be y = -3/2x + 7/2

Step-by-step explanation:

In order to find this, we must first use the slope formula with the two point to find the slope.

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

m = (5 - -1)/(-1 - 3)

m = 6/-4

m = -3/2

Now that we have the slope, we can use that and either point in point-slope form. Then we solve for y.

y - y1 = m(x - x1)

y + 1 = -3/2(x - 3)

y + 1 = -3/2x + 9/2

y = -3/2x + 7/2

d

step-by-step explanation:

d

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