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Question 593787: I have an algebra question. On my worksheet, it says "Determine a relationship between the x- and y-values. Write an equation." I know how to do that, but for the second problem, the ordered pairs are (2,3), (3,5), (4,7), and (5,9). I put them in a table and it looks like the relationship is a sequence, because as you go up, you add 1 to 2 to make 3, and then you add 2 to 3 to make 5, and so on. How would you write this as an equation? (i.e. y=x+3)
This is what the problem looks like:
x 2 3 4 5
y 3 5 7 9
Found 2 solutions by AnlytcPhil, Sarpi:
Answer by AnlytcPhil(1810)   (Show Source):
You can put this solution on YOUR website!
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
Answer by Sarpi(32)  (Show Source):
You can put this solution on YOUR website! X Y
2 3
3 5
4 7
5 9
From the data, X moves in steps of 1 point and Y in steps of 2 points. Therefore, if X is increased by 1, Y is increased by 2.
=> The figures are in sequence, so we need to determine how to go from X to Y, that is 2 to 3, 3 to 5, 4 to 7, and 5 to 9.
From this, it can be seen that the changes between X and Y are 1, 2, 3, and 4 respectively.
Interpretation;
from X value of 2 to Y value of 3 = 2+1
from X value of 3 to Y value of 5 = 3+2
from X value of 4 to Y value of 7 = 4+3
from X value of 5 to Y value of 9 = 5+4 ; where these adding numbers are the value of the previous X
(2+prev. X value = 3, 3+prev X value = 5 and so on)
Mathematically, the relationship is Y = Current value of X + Previous value of X
Y = X + (X - 1)
Y = X + X -1
Y = 2X - 1
Verification:
if X = 2 then Y = 2*2 - 1 = 3
if X = 3 then Y = 2*3 - 1 = 5
if X = 4 then Y = 2*4 - 1 = 7
if X = 5 then Y = 2*5 - 1 = 9
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