Which equation represents a line that passes through the two points in th table? ​

Part (a)

Lets say we had the two general vectors

u = (a,b)

v = (c,d)

The dot product is

u dot v = a*c + b*d

Apply that rule to these specific vectors

u = (5, -2)

v = (0, 1)

So we get

u dot v = 5*0 + (-2)*1

u dot v = 0 - 2

u dot v = -2

Therefore,

(u dot v)*w = -2*(-1, -3)

(u dot v)*w = ( -2*(-1), -2(-3) )

(u dot v)*w = (2, 6)

 (2, 6)

Part (b)

u = (5, -2)

5u = 5*(5, -2)

5u = (5*5, 5*(-2))

5u = (25, -10)

5u dot v = (25, -10) dot (0,1)

5u dot v = 25*0 + (-10)*1

5u dot v = 0 - 10

5u dot v = -10

-10