Interpolate along route

[NancyStence]

I have point data along lines that represents certain values at those locations on a pipeline.  The points are not currently snapped to the lines but are adjacent to the lines.  I would like to interpolate between the points along the line, assuming a linear relationship between distance and value.  The goal is to represent the interpolated values between the known points, which may be 1000 feet apart.  Is there a tool that will do this?  I have looked through all the interpolation tools in spatial analyst but all of the tools return a surface, whereas I want a line with values along it.

Thanks,

[JeffreySwain]

If you had a surface created with a Spline to force the surface to conform to the point elevations and interpolate between, then you could use the Extract Values to Point tool in Spatial Analyst or if you had 3d Analyst you could use the Add Surface Information tool or Interpolate shape to make the line 3d.