Why is segment B’C on the same line as its corresponding side, segment BC?

Ineed the rest of the question and answers

Iknow one of the answers is a and maybe b but not 100% sure about b

(6,1)(5,4)slope = (4 - 1) / (5 - 6) = 3/-1 = -3y = mx + bslope(m) = -3use either of ur , = 6 and y = 1now sub and find b, the y int1 = -3(6) + b1 = -18 + b1 + 18 = b19 = bso ur equation is : y = -3x + we need it in standard formy = -3x + 3x to both sides3x + y = 19 < == standard form