Final answer:
The equation of the line that passes through (5, -2) and is perpendicular to y = -x - 3 is y = x - 7.
Step-by-step explanation:
To find the equation of a line that passes through the point (5, -2) and is perpendicular to the line y = -x - 3, first, we need to understand that perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is -1, so the slope of the perpendicular line will be 1 (negative reciprocal of -1 is 1).
Now, using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line (5, -2) and m is the slope (1 in this case), we can plug in the values:
y + 2 = 1(x - 5)
Simplifying this, we get:
y + 2 = x - 5
Finally, subtract 2 from both sides to get the line in slope-intercept form: y = x - 7.
So the equation of the line that is perpendicular to y = -x - 3 and passes through the point (5, -2) is y = x - 7.