Final answer:
To find a line perpendicular to line m with the equation y - 1 = 4/5(x - 3), use the negative reciprocal of its slope 4/5, which is -5/4. A possible equation for a line perpendicular to line m is y - 1 = -5/4(x - 3).
Step-by-step explanation:
The equation of line m is given by y - 1 = 4/5(x - 3). This equation is in point-slope form, where the slope (m) of the line is 4/5. To find a line perpendicular to line m, we need to use the negative reciprocal of its slope. The negative reciprocal of 4/5 is -5/4. Therefore, any line with a slope of -5/4 will be perpendicular to line m.
If we want to write the equation of a line that is perpendicular to line m, we can assume it passes through a point (we can use the same point (3,1) from line m for simplicity) and has a slope of -5/4. Using the point-slope form, the equation would be written as y - 1 = -5/4(x - 3).