For this case we have that by definition, the 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 cut-off point with the y axis
We have to, if two lines are parallel then their slopes are equal.
If we have [tex]y = -x-2[/tex]with slope [tex]m_ {1} = - 1[/tex], then a parallel line will have slope [tex]m_ {2} = - 1.[/tex]
Thus, the equation of the parallel line is of the form:
[tex]y = -x + b[/tex]
We substitute the given point and find "b":
[tex]-2 = - (2) + b\\-2 = -2 + b\\-2 + 2 = b\\b = 0[/tex]
Finally, the equation is:
[tex]y = -x[/tex]
Answer:
[tex]y = -x[/tex]
