Final answer:
To find the equation of a line perpendicular to another and passing through the point (-2, 3), we use the negative reciprocal of the original slope, which is -1/3, and apply the point-slope formula, resulting in the equation y = -1/3x + 7/3.
Step-by-step explanation:
The student is tasked with finding the equation of a line that is perpendicular to a given line and passes through a specific point (-2, 3). To determine the slope of the new line, we use the negative reciprocal of the original line's slope. Since the original line is not specified, we'll refer to Figure A1 which presents a line with a slope (m) of 3. Hence, the slope of the perpendicular line would be -1/3. We can then use the point-slope formula to find the equation of the new line:
y - y1 = m(x - x1)
Plugging in the point (-2, 3) and the slope -1/3, we get:
y - 3 = (-1/3)(x - (-2))
Expanding and simplifying this, we get the equation of the desired line:
y = -1/3x + 7/3