Question 400208
How do I find the equation of the line joining the following pairs of points:
1. (1,8) and (-1,-20)
2. (2,-1) and (3,5)

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These equations can take one of two forms: slope-intercept or point-slope. I will do the former, y=mx+b, m being the slope and b the y-intercept. The problem is to find the slope,m, and the  y-intercept,b.

1. slope=change in y/change in x or rise/run.
        =8-(-20)/1-(-1)=28/2=14
   y=14x+b
   using first ordered pair(1,8) (using either pair is ok)
   8=14(1)+b
   b=8-14=-6
   equation: y=14x-6
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2. slope=change in y/change in x or rise/run.
        =(-1-5)/(2-3)=-6/-1=6
   y=6x+b
   using first ordered pair(2,-1) (using either pair is ok)
   -1=6(2)+b
   b=-12-1=-13
   equation: y=6x-13

See these two equations on the graph below:

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{{{ graph( 300, 200, -6, 5, -20, 10, 14x-6,6x-13) }}}