Let A(1,2), B(6,1) and C(7,8) be three points in the plane. Find the equation of the line passing through point C and through the midpoint of the line segment AB. Write answer in the form

ax + by + c = 0.

I found slope of AB to be (-1/5).

I also found the midpoint of AB to be (7/2, 3/2).

I then decided, for unknown reasons, to calculate the slope of the perpendicular bisector to be 5.

I then plugged 5 and the midpoint into point-slope formula and got the wrong answer. Trying a second time through guessing, I decided to plug 5 and point C into the point-slope formula and again got the wrong answer. The textbook does not give a sample representing the question above or else I can do it in 5 minutes.

What are the steps leading to the right equation? I just want the steps to see if I can work it out alone. Thank you very much.