This is a linear polynomials(or first degree polynomials). It is a form of y=ax+b.The line passes through (4, 5) and (2, 2), so we can build a dualistic equation: ｛5=4k + b
｛2=2k + b
solve this equation, we can know that k=1.5 and b=-1, then the function is y=1.5x - 1, D is correct.
If y=1.5x - 1, then y-2=1.5x-1-2=1.5x-3=1.5(x-2), so A is correct, too.
y-4=1.5x-1-4=1.5x-5, so B is incorrect.
y-5=1.5x-1-5=1.5x-6=1.5(x-4), so C is correct. Now we can know the answer: the correct options are A,C and D Sorry my English expression is not very good, but hope it can help you:)