Final answer:
The equation of the line that is perpendicular to a given line and passes through a given point can be found using the point-slope form of a linear equation.
Step-by-step explanation:
To find the equation of a line that is perpendicular to line m and passes through the point (3,2), we need to determine the slope of line m first. Let's say the slope of line m is represented by m1. Since the line that is perpendicular to line m has a slope that is the negative reciprocal of m1, we can determine the slope of the perpendicular line as -1/m1.
Now, we can use the point-slope form of a linear equation to find the equation of the perpendicular line: y - y1 = m2(x - x1), where (x1, y1) is the given point and m2 is the slope of the perpendicular line.
Using the point (3,2), we substitute x1 = 3, y1 = 2, and m2 = -1/m1 into the equation: y - 2 = -1/m1(x - 3).
Thus, the equation of the line that is perpendicular to line m and passes through the point (3,2) is y - 2 = -1/m1(x - 3).