How to get xy data from plot?

Hello,

I have 3 data sets, with 2 of them for the same variable. Say one y matrix and two matrices for x, with different values of x in both but all of them lie between 0,1. i have a plot for x1,y. Now i need to find the values of y when the values of x are those specifies in x2. Any ideas on how i could go about this? Thanks!

eg: 
x1=0,3,5,6,7
corresponds to
y1=0,6,10,12,14
secondary x matrix
x2=1,4,5,7,8,9
y2=?

the relationship between x1 and y1 is the same as x2 and y1 since x1 and x2 both represent the same variable. now i want to obtain values of the function at x2.

note: i have already tried using curve fitting functions but the functions i get for even a 10th order equation are not accurate enough.