I laid my hands on Nova's DS prep Course. and started seeing some places where a mathematical equation was given straight away without the intermediate steps. Does any one know how I can fill in the blanks in the following content of that guide?

The author

Every time x increases (decreases) by a particular value, y decreases (increases) by two times that value (this is the system description). What is the value of x when y is 3? (1) When y is 1, x = 3. (2) When y is 2, x = 1.
• Statements (1) and (2) above are constraints that limit the system. For example, the shape of the hidden system in the problem (question setup) is x + 2y = c. So, the system blah blah... |

Speaking intuitively too, the relation between x and y appears to be positive monotonous and hence the line will have a positive slope. This is the first proof of contradiction for the equation above.

To be slightly more mathematical, if (x1,y1) and (x2,y2) are two points that follow the above rule,then (y2-y1) = 2(x2-x1) and indirectly this means that the equation for the line is y = 2x + k for some real number k.

How does the author arrive at the equation (which I highlighted in

italic bold above? The main problem is that my equation has a slope that is inverse to that of the author's claim. But as the author does not show the intermediate steps, this part of the book defeats me.

Any help?

Regards

Rahul

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Regards

Rahul