Final answer:
The equation of the line perpendicular to y = x + 5 and passing through (-1, -5) is y = -x - 4.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The equation of the given line is y = x + 5, which has a slope of 1. The negative reciprocal of 1 is -1, so the slope of the perpendicular line is -1.
Since the perpendicular line passes through the point (-1, -5), we can use the slope-intercept form of a linear equation, y = mx + b, to find the equation of the line. Plugging in the point and the slope, we get y = -1x + b. Substituting the coordinates of the point into the equation, we find that -5 = -1(-1) + b. Solving for b, we get b = -4. Therefore, the equation of the line perpendicular to y = x + 5 and passing through (-1, -5) is y = -x - 4.