Question 593787
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x 2 3 4 5
y 3 5 7 9

There are more than one way to do this kind of problem.
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First way:

Look at (2,3).  If you add 1 to 3 you get 4, and 4 is twice 2.

Look at (3,5).  If you add 1 to 5 you get 6, and 6 is twice 3.

Look at (4,7).  If you add 1 to 7 you get 8, and 8 is twice 4.

Look at (5,9).  If you add 1 to 9 you get 10, and 10 is twice 5.

Now take the general case (x,y) and say the same thing about it:

Look at (x,y).  If you add 1 to y you get y+1, and y+1 is twice x.

Write that as an equation:

             y+1 = 2x

which simplifies to

               y = 2x - 1
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Second way:

Look at the point (2,3).  If you double 2 you get 4, and 4 is 1 more than 3.

Look at the point (3,5).  If you double 3 you get 6, and 6 is 1 more than 5.

Look at the point (4,7).  If you double 4 you get 8, and 8 is 1 more than 7.

Look at the point (5,9).  If you double 5 you get 10, and 10 is 1 more than 9.

Now take the general case (x,y) and say the same thing about it:

Look at the point (x,y).  If you double x you get 2x, and 2x is 1 more than y.

Write that as an equation:

                 2x = y + 1

which simplifies to

             2x - 1 = y                    

or 

                  y = 2x - 1

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Third way:

Look at the point (2,3).  If you subtract 2 from 3 you get 1, and 1 is 1 less than 2.

Look at the point (3,5).  If you subtract 3 from 5 you get 2, and 2 is 1 less than 3.

Look at the point (4,7).  If you subtract 4 from 7 you get 3, and 3 is 1 less than 4.

Look at the point (5,9).  If you subtract 5 from 9 you get 4, and 4 is 1 less than 5.

Now take the general case (x,y) and say the same thing about it:

Look at the point (x,y).  If you subtract x from y you get y-x, and y-x is 1 less than x.

Write that as an equation:

              y-x = x-1

which simplifies to

                y = 2x - 1
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There are even other ways to do it but you always get y = 2x - 1



Edwin</pre>