What is the slope of the hypotenuses of the triangles in simplest form?

3

First-quadrant graph showing a ray through the origin and the points (3, 1), (6, 2), and (18, 6). Two triangles each have their longest sides with endpoints along the line, a vertical leg, and a horizontal leg. The first triangle has a longest side with endpoints at (3, 1) and (6, 2). The second triangle has a longest side with endpoints at (6, 2) and (18, 6).

Question

What is the slope of the hypotenuses of the triangles in simplest form?
 
 
3
 
 
   First-quadrant graph showing a ray through the origin and the points (3, 1), (6, 2), and (18, 6). Two triangles each have their longest sides with endpoints along the line, a vertical leg, and a horizontal leg. The first triangle has a longest side with endpoints at (3, 1) and (6, 2). The second triangle has a longest side with endpoints at (6, 2) and (18, 6).