The equation of the given line is
y = mx + c
where
m = slope
c = y intercept
The equation of the given line is
y = 3x - 8
By comparing both equations,
m = 3
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The negative reciprocal of 3 is - 1/3. Thus, the slope of the perpendicular line passing through (2, 5) is - 1/3
We would fnd the y intercept, c by substituting m = - 1/3, x = 2 and y = 5 into the slope intercept equation. We have
5 = - 1/3 * 2 + c = - 2/3 + c
c = 5 + 2/3 = 17/3
Thus, the equation of the perpendicular line is
y = - x/3 + 17/3