SOLUTION: What is the angle between the horizontal (x) axis and the line containing the points (2,8) and (4,9)?

We observe that the angle q that the green line makes with the 
x-axis is the same size angle as the angle marked q in the little right
triangle up where the two given points are.

In that little right triangle we see that the opposite side of q is 
1 unit long and the adjacent side to q is 2 units long, 
so we use the trig function that involves opposite and adjacent:

                 tan(q) = 
                 tan(q) =   

Use the inverse tangent fuction on the calculator and get

                 q = 26.56505118° = 26°33'54"

I hope you observed that the tangent of that angle q is the slope
of the green line.
                                                      
Edwin