Final answer:
To find the equation of a line perpendicular to the given line and passing through the given point, determine the slope of the given line, find the negative reciprocal of that slope, and use the point-slope form of a line.
Step-by-step explanation:
To find the equation of a line perpendicular to the given line and passing through the given point, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line has an equation of y - 1 = x + 5, which can be rewritten as y = x + 6. The slope of this line is 1. The negative reciprocal of 1 is -1/1, which simplifies to -1. So, the slope of the perpendicular line is -1. Now, we can use the point-slope form of a line to find the equation.
The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values (-5, 1) as the point and -1 as the slope, we get the equation y - 1 = -1(x - (-5)), which simplifies to y - 1 = -1(x + 5). This is the equation of the line that is perpendicular to the given line and passes through the given point.