Final answer:
The line perpendicular to y = -x + 2 has a slope of 1. Using the point-slope form with the point (-5, 2), the equation is y = x + 7. However, this is not reflected in the answer choices given.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another, you need to determine the new line’s slope. For a line perpendicular to y = -x + 2, the slope will be the negative reciprocal of -1, which is 1. Using the point (-5, 2) that the new line passes through, you can employ the point-slope form:
y - y1 = m(x - x1)
Here, (x1, y1) is the point (-5, 2) and m is the slope which is 1. Plugging in these values gives:
y - 2 = 1(x + 5)
Simplifying further yields:
y = 1x + 5 + 2
y = x + 7
However, none of the answer choices match this equation, which suggests there may be an error in the choices provided or in the interpretation of the question. Perpendicular lines should have slopes that are negative reciprocals, so if the original line has a slope of -1, the correct perpendicular line should have a slope of 1.