a) Derivation of the general equation for Interpolation: Develop from scratch the equation forinterpolation you need to develop the equation in terms of x,X1,X2,y,y1,Y2 etc... no numbers, you need toderive the general expression for y. Show every single step of this process, add comments when necessary toexplain what you are doing, this procedure must show that you understand very well how to derive thisequation. Also mention under which condition/assumption this equation is valid.b) Interpolation: Using the equation you derived in a), estimate the dynamic viscosity liquid water in(kg/m-s) at 31.7 °C. Show ALL your work in detail, write a statement indicating if the results makes sense.c) Extrapolation: Estimate the enthalpy of vaporization for water in (kJ/kg) at 57.6 °C. Derive a newequation if necessary. Show ALL your work in detail, write a statement indicating if the results makes sense.

Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question. Linear interpolation is a method of curve fitting. It is the method for finding new data points within the range of given discrete data points. It is assumed that all these three points are colinear in nature. This means that these three points form a straight line.Assume the two known points of the coordinates, A(x1,y1) & B(x2,y2). We need to find a third coordinate point C(x,y). As the line is a straight line, the slope of the line remains constant. The slope of the line from points A and B, m=y2-y1x2-x1 The slope of the line from points A and C, m=y-y1x-x1 Equating the above 2 equations, y-y1x-x1=y2-y1x2-x1 y=y1+x-x1y2-y1x2-x1The equation for y is, y=y1+(x-x1)y2-y1x2-x1