SOLUTION: hi i wanna know about satisfies a liner funcation like this question i dont know how to solove it (5,1),(4,4),(3,9),(2,16),(1,25) and have a nice bye

Question 789021: hi i wanna know about satisfies a liner funcation
like this question i dont know how to solove it
(5,1),(4,4),(3,9),(2,16),(1,25)
and have a nice bye
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
That is not a linear relation.
Not knowing what you need from the data, it is hard to figure out what to tell you. The answer you need is different if you are studying calculus, arithmetic sequences, or strategies for a standardized test. (And maybe your situation is none of the above).

If you just need to see the pattern:
The first numbers (the x's) in those (x,y) pairs are consecutive numbers, counting down from 5,
while the second numbers (the y's) are consecutive squares:
, , , , and .

If you are looking for a function or relationship between y's and x's in the (x,y) pairs:
If it were linear, as the x increases by 1
(from (1,25) to (2,16), from (2,16) to (3,9), from (3,9) to (4,4), and from (4,4 to (5,1)),
y would change by the same amount each time.
Instead, y decreases by 9, 7, 5, and 3 units respectively.
There is clearly a pattern, but it is not linear.
In fact, it is a quadratic function.
To continue the pattern, from (5,1) (with x=5 and y=1),
as we increase x by 1 each time,
we would subtract from the y values, 1, -1, -3, etc,
getting to y=1-1=0 for (6,0),
y=0-(-1)=0+1=1 for (7,1),
y=1-(-3)=1+3=4 for (8,4), and so on.
The plotted data points are on a symmetrical curve called a parabola:

The function is

If this was related to sequences, calculus/pre-calculus, or physics, there are too many possibilities:
You could see the y's as separate sequences.
The y's could be the sums of an arithmetic sequence (series).
The x's and y's could indicate the position of a moving object.
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