Equation of a line

This is a BMAT question from 2021, the correct answer is letter e), i got it right but i had to draw the graph and did it more or less by try and error, by drawing the graph of the reflected line and found some points for x and y, until it made sense the position of the points of the new line. Is there any faster and more accurate way to solve it?

The line with equation y = –2x + 1 is reflected in the line with equation x = 2 Which of the following is the equation of the new line?
A y=− 1/2x −2
B y=−1/2x+1
C y=−1/2x+7/4
D y=−1/2x+3
E y=2x–7
F y=2x–1
G y=2x+1
H y=2x+3


Reflection on the origin should be -f(-x) but I’m having trouble finding the correct answer using this
Can anyone solve with this?

hey this question says reflected in the line x=2 , so that would be a vertical line at x=2 where you reflect the equation from that line . the rule that says f(x)= f(-x) is for reflection across y axis itself since the line that we will reflect about is x=0 we dont need to consider anything just the sign of slope , and you would find the answer easily by just multiplying f(x) by f(-x). let me know if you dont get it !