Write the point-slope form of the line that passes through (5, 5) and is perpendicular to a line with a slope of . Include all of your work in your final answer. Type your answer in the box provided to submit your solution.
A line that is perpendicular to a line with slope m will have a slope of -1/m. Since the given line has a slope of , the perpendicular line will have a slope of -1/().
We are also given that the perpendicular line passes through the point (5, 5).
Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute in the values:
y - 5 = (-1/) * (x - 5)
y - 5 = (-1/)*(x - 5)
y - 5 = -x/ + 5/
y = -x/ + 5/ + 5
Therefore, the point-slope form of the line that passes through (5, 5) and is perpendicular to the line with a slope is y = -x/ + 5/ + 5.