If a line perpendicular to 2y=x+5 that passes through (2,1) using the slope - intercept form

Slope of 2y = x + 5:-

This is y = 0.5 x + 2.5 in slope intercept form so its slope = 0.5

Slope of the line perpendicular to it = - 1 / 0.5 = - 2

it passes through (2, 1) so we have

y - 1 = - 2 (x - 2)

y = - 2x + 4 + 1

The answer is y = - 2x + 5