Final answer:
To write the equation in point-slope form, find the slope of the perpendicular line, which is the negative reciprocal of the original line's slope. In this case, it's -1/3. Then, use the point (1, 1) to write the equation: y - 1 = (-1/3)(x - 1).
Step-by-step explanation:
To write an equation in point-slope form that is perpendicular to a given line and passes through a specific point, we need to use slope-intercept form and the concept of perpendicular slopes. First, let's clarify the original equation. It seems there is a typo in it, as the equation of a line is typically given in y = mx + b form, where m is the slope and b is the y-intercept. Based on the information provided, we can assume that the original line's equation is y = 3x + 9, which has a slope of 3.
Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of the line perpendicular to the original line will be -1/3 (since the negative reciprocal of 3 is -1/3).
Given that the line must pass through the point (1, 1), we can write the equation in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope. Plugging in our values, we get:
y - 1 = (-1/3)(x - 1).
This is the desired equation in point-slope form.