Triangle ABC has vertices A(0,6) B(4,6) C(1,3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter, including any necessary points or slope you had to derive.

For line B to AC:  y - 6 = (1/3)(x - 4);  y - 6 = (x/3) - (4/3); 3y - 18 = x - 4, so 3y - x = 14For line A to BC:  y - 6 = (-1)(x - 0);  y - 6 = -x, so y + x = 6Since these lines intersect at one point (the orthocenter), we can use simultaneous equations to solve for x and/or y:(3y - x = 14) + (y + x = 6) =>  4y = 20, y = +5;  Substitute this into y + x = 6:  5 + x = 6, x = +1So the orthocenter is at coordinates (1,5), and the slopes of all three orthocenter lines are above.