Find an equation of the line that goes through the points (7,-42) and (10,-57). write your answer in the form y = m x + b y = m x + b .

y = -5x - 7

Step-by-step explanation:

What's the slope of this line?  Going from  (7,-42)  to  (10,-57), we see x increasing by 3 and y decreasing by 15.  Thus, the slope is m = rise / run = -15/3, or m = -5.  

Now subst. -42 for y in y = mx + b, -5 for m and 7 for x:

-42 = -5(7) + b.  Thus, b = -42 + 35, or b = -7. and the equation of this line is thus   y = -5x - 7.

Check:  if x = 10, does this equation yield y = -57?  Yes

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