There are infinitely many rules that would represent that,
but the most obvious one is



because , , , 

But don't allow your teacher to tell you that is the ONLY one!

For we can always find a nth-degree polynomial that will go through
any n-1 points.

For instance this answer 



is just as good, although
not quite as simple:

Substitute those x-values in that and you will also get the y-values.

-------------------------

Write the rule that represents the function 
x = 0, 1, 2, 3, 4
y = -7, -2, 3, 8, 13

We notice that 

-7+5=-2, -2+5=3, 3+5=8, 8+5=13

So we suspect that this is linear, of the form y=mx+b

So we try 

y=mx+b

Substitute (0,-7)

-7=m(0)+b
-7=b

So y=mx-7

Substitute (1,-2)

-2=m(1)-7
-2=m-7
5=m

so the obvious answer is y=5x-7
and if you substitute all those s-values you'll get
the corresponding y-values.

But there are many other functions that work too.

Edwin