Final answer:
The equation of the line through (-2, 2) that is parallel to y = -x - 2 is y = -x.
Step-by-step explanation:
To write the equation of a line that is parallel to a given line and passes through a specific point, you need to ensure that the new line has the same slope as the given line. Given the line y = -x - 2, the slope of this line is -1 because the coefficient of x is -1 in the slope-intercept form y = mx + b, where 'm' represents the slope.
The equation of the line that is parallel to y = -x - 2 and passes through the point (-2, 2) will have the same slope, which is -1. We use the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through, and 'm' is the slope.
So, for the point (-2, 2), the equation becomes:
y - 2 = -1(x + 2)
y - 2 = -x - 2
Therefore, adding 2 to both sides gives us the final equation: y = -x.