How to find slope of any given line segment?

 Best   I'll make one up and explain how to do it. 

Lets say your two points are (2,6) and (-4,7) 

To start with you need to use the point-slope formula which is y2-y1/x2-x1 

Remember (x,y), Thus we have 

7-6/-4-2 = 1/-6; So out slope is -1/6 

Now lets use the following equation y = mx+b to solve for b which is the y-intercept. By substitution of either order pair we can solve for b 

6 = 2(-1/6)+b; distribute the 2 
6 = -2/6+b; add 2/6 to each side to isolate b 
6+2/6 = b; put 6 over 1 
6/1+2/6 = b; get a common denominator between 6/1 and 2/6 which is 6 
6(6/1)+2/6 = b ; distribute 
36/6+2/6 = b; add these up 
38/6 = b; reduce to lowest terms by dividing by 2 to each 
19/3 = b 

So our final equation is y = -1/6x+19/3