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.

Answer 1

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)