Question

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 or use the upload option to submit your solution.

Answer 1

The point-slope form of the line that is perpendicular to a line with a slope of 1 and passes through the point (1, -5) is y + 5 = -1(x - 1).

Step-by-step explanation:

To write the point-slope form of the line that passes through the point (1, -5) and is perpendicular to a line with a slope of 1, we first need to determine the slope of the perpendicular line. Since the given slope is 1, the slope of the line perpendicular to it will be the negative reciprocal. Therefore, our slope is -1.

The point-slope form equation is:

y - y1 = m(x - x1)

By substituting our known values (x1 = 1, y1 = -5) and the slope (m = -1), the point-slope form of the equation becomes:

y - (-5) = -1(x - 1)

Simplifying the equation, we get:

y + 5 = -1(x - 1)

Answer 2

a perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So if we have a slope of 1 or 1/1. our perpendicular line needs a slope of -1.

y - y1 = m(x - x1)
slope(m) = -1
(1,-5)...x1 = 1 and y1 = -5
now we sub...pay close attention to ur signs
y - (-5) = -1(x - 1)....not done yet
y + 5 = -1(x - 1)...or it can also be written as : y + 5 = - (x - 1)