Answer:
y=x-2
Step-by-step explanation:
If you have drawn the graph of [tex]y = x^2 - 3x + 1[/tex].
To determine the equation of the line which  should be drawn to solve the equation:  x² - 4x +3=0
Simply carry out the subtraction: [tex]x^2 - 3x + 1 -(x^2 - 4x +3)[/tex]
[tex]\implies x^2 -3x + 1-x^2 + 4x -3 \\= x^2 - x^2+ 4x - 3x-3 + 1\\=x-2[/tex]
The equation of the line which should be drawn is: y=x-2
What this means is simply:
If
[tex]y = x^2 - 3x + 1$ and $y=x-2,$ then:\\x^2 - 3x + 1=x-2\\x^2 - 3x + 1-x+2=0\\x^2 - 4x + 3=0[/tex]
