Final answer:
The equation of a line parallel to y = -5x + 2 has the same slope of -5. Therefore, it can be expressed as y = -5x + b, where 'b' is any y-intercept.
Step-by-step explanation:
The equation of a line that is parallel to another can be determined by having the same slope as the original line. In this case, the given line is y = -5x + 2.
The slope of this line is -5.
Any line that is parallel to this line must also have a slope of -5.
Thus, the general form of the equation of a line parallel to the given line is y = -5x + b, with 'b' being any real number which represents the y-intercept of the new line.
For example, if we pick a y-intercept of 3, the equation of our parallel line would be y = -5x + 3.
This is because the slope is preserved and only the y-intercept 'b' changes.