Given that the points (16,-5) and (-40,16) lie on a line, what is the equation of the line?

(16,-5) and (-40,16)

We need to find the slope of this line, first...

This is gven by ....    change in y / change in x    =     [16 - (-5)]  / [-40 - 16 ] = 

21 / -56   =  -21/ 56 = -3/8

Now, using the slope-intercept form, we have

y + 5 = (-3/8)(x - 16) 

y + 5 = (-3/8)x + 48/8 

y = (-3/8)x + 6 - 5

y = (-3/8)x + 1

P.S....check this with the second set of points.....I believe you'll find that they work...