we are asked to find the equation of the line that passes through (2,5) and is perpendicular to y = 2x - 8
when 2 lines are perpendicular to each other the slope of one line is the negative reciprocal of the other line.
the slope of the perpendicular line is 2, then the slope of the line we are asked to find should have the negative reciprocal of 2 , that is -1/2
m = -1/2
We know x and y coordinates of one point, we can substitute
y = mx + c
y = 5, x = 2
5 = -1/2 *2 + c
5 = -1 + c
c = 6
the equation of the line is
y = -1/2x + 6