SOLUTION: if (a,0) ,(0, b) (1,1) are collinear find relation between a& b

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Question 882665: if (a,0) ,(0, b) (1,1) are collinear find relation between a& b
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Collinear; the slope between any pair of the three points is the same, allowing....

%280-1%29%2Fa-1%29=%28b-1%29%2F%280-1%29 and %280-b%29%2F%28a-0%29=%28b-1%29%2F%280-1%29;
1%2F%281-a%29=1-b and -b%2Fa=1-b;
1=%281-a-b%2Bab%29 and -b=a-ab;
ab-a-b=0 and a-ab+b=0
-a-b+ab=0 and a+b-ab=0
a+b-ab=0

Simple sense about some common number facts may allow seeing that you may be able to see that if a=b=0, this will work, and if a=b=2, this will also work. Any other ways you see? Try testing any pick for a and find the corresponding value for b. Will the combination also work?