Answer: The given line has a slope of -1, since its equation is y = -x + 5. The line that is perpendicular to this line will have a slope that is the negative reciprocal of -1, which is 1. So, we know that the equation of the line we're looking for will have a slope of 1.
To find the equation of this line, we need to use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
We know that the point (-2, 5) is on the line we're looking for, and we know that the slope of the line is 1. So we can substitute these values into the point-slope form:
y - 5 = 1(x - (-2))
Simplifying, we get:
y - 5 = x + 2
Adding 5 to both sides, we get:
y = x + 7
Therefore, the equation of the line that passes through the point (-2, 5) and is perpendicular to the line y = -x + 5 is y = x + 7.
Explanation: