the slope of the line y = 3x/4 + 3 is 3/4

let the slope of the perpendicular line be 'm'

if the lines are perpendicular then when you multiply their slopes, you get -1 thus

m*(3/4) = -1

m = -(4/3)

click here to see the solution of the equation for m

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all the lines with slope -(4/3) are perpendicular to the line y = 3x/4 + 3

they can be written as y = -4x/3 +b, where b is the y-intercept of the line

for example one such line is for b = 1

y = -4x/3 + 1