True or False: If we have an integer primal solution with cost C and a fractional dual solution with cost at least C/2, the size of the vertex cover corresponding to the primal solution is at most twice the size of the smallest vertex cover. Briefly justify your answer

True

Step-by-step explanation:

The size of the vertex cover is atleast twice the size of the maximum edge. Vertex must contain atleast one vertex from the matched edge. Vertex are never the strong dual solutions of each other.

4x + y = 10

Step-by-step explanation:

The point-slope form of the equation of a straight line is y - k = m(x - h).

Letting m = -4, 1 = h and 6 = k, we get                               y - 6 = -4(x - 1).

Now we must rewrite this in standard form.  Do this:  Carry out the multiplication.  We get y - 6 = -4x + 4.

Now add 6 to both sides, obtaining

                                         y = -4x +10

Finally, add 4x to both sides, obtaining:

                                          4x + y = 10.  This is the desired equation in standard form.