For this case we have that an equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
They give us the following information:
[tex]m = -2\\b = 3[/tex]
Then the line is:
[tex]y = -2x + 3[/tex]
They ask us to find a parallel line. By definition, if two lines are parallel then they have the same slope. Thus, the line sought is of the form:
[tex]y = -2x + b[/tex]
We look for the cut point "b" substituting the point where the line passes: [tex](2,2)[/tex]
[tex]2 = -2 (2) + b\\2 = -4 + b\\2 + 4 = b\\b = 6[/tex]
Finally, the line is:
[tex]y = -2x + 6\\y + 2x = 6[/tex]
Answer:
Option A
