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