Where indicated below, complete the function, linspline$(),$ which takes two input vectors of data points x and y$,$ of any length n $($either both column or row$),$ and scalar input, a$.$ It computes output, s$,$ which is $,$ the linear function,, evaluated at a:

where a is on $.$

$($This function is one linear function $($i$.$e$.,$ one line$)$ in the piecewise linear function on the entire interval,:

$)$

i$)$ The function linspline$()$ will first search for the value of k$,$ where $.$ To accomplish this, linspline$()$ will call a modified version of the binary search function disussed in class. Modify the code per the instructions in the comments below.

ii$)$ Then, the code will evaluate for just the interval $.$ For example, if the value of were between and $($k$=8),$ then it would only evaluate s $=.$ Assume that and $,$ but that are not necessarily evenly$-$spaced.