Answer:
D ; y = (4/3)x + 2
Explanation:
The general form of the equation of a straight line is;
y = mx + b
where m is the slope and b is the y-intercept
Now, let us represent the given equation in this general form
We have this as;
4y= -3x + 12
divide through by 4
y = -3/4x + 3
Now, the slope of this equation is -3/4
Mathematically, when two lines are perpendicular, the product of their slopes is -1
let us have the slope of the second equation as m2
-3/4 * m2 = -1
-3m2 = 4 * -1
m2 = -4/-3
m2 = 4/3
so, the equation that is perpendicular will have its slope as 4/3
Looking through the options given as we have the equations in the general form, the equation D is the correct answer
D ; y = (4/3)x + 2