Question 565991
(k,2k-3) and (2-k,k-2), 

Slope m = (y2-y1)/(x2-x1)

m={{{((k-2)-(2k-3))/((2-k)-k))}}}


m= {{{(k-2-2k+3)/(2-2k)}}}

m={{{(-k+1)/(2(1-k))}}}


m= {{{((1-k))/(2(1-k))}}}

m= 1/2


slope = 1/2 & point ( (k,(2k-3))


2k-3= (1/2)*k +b

2k-3-(1/2)k=b

multiply equation by 2
4k-6-k=2b
(3k-6)=2b
3(k-2)=2b
3(k-3)/2 =b

Frame the equation

y = (1/2) x +3(k-2)/2