Write the point-slope form of the line that passes through (1, -5) and is perpendicular to a line with a slope of 1. Include all of your work in your final answer. Type your answer in the box provided to submit your solution.
We are given that the line we want to find is perpendicular to a line with a slope of 1. Perpendicular lines have slopes that are negative reciprocals of each other. So the slope of the line we are looking for is -1.
We also know that the line passes through the point (1, -5).
The point-slope form of a line is y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of a point on the line, and m is the slope of the line.
Plugging in the values from the given point and the slope we found, we get:
y - (-5) = -1(x - 1)
Simplifying, we have:
y + 5 = -x + 1
Rearranging the equation to get it in slope-intercept form (y = mx + b), we get:
y = -x - 4
So the point-slope form of the line that passes through (1, -5) and is perpendicular to a line with a slope of 1 is:
y + 5 = -1(x - 1)