Determine deflection values at every $1$ft ordinates. Problem $1$: Conjugate Beam Method

$($a$)$ Using Conjugate Beam Method evaluate the equation for Deflection for the beam given in Figure $1.$

Figure $1.$

$($b$)$ Using the computed equation from question $1($a$)$ compute the deflection value for given data. Determine the deflection at every $1ft.$

Given Data: $P=10-$kip, $L=20ft,a=15ft,b=5ft,E=29,000$KSI,$I=160I{n}^4.$