The equation in given as ;
2y = -3x + 1
This can be written as ;
y= -3/2 x + 1/2
This means the equation has a gradient of -3/2
Let this slope , be , ---------m1
For perperdicular lines , the product of their slopes = -1 .This means if the other line has a gradient of m2 then : m1 * m2 = -1
So from the answers :
i) y= 2/3 x - 1 the slope is 2/3
m2 = 2/3
m1 * m2 = -1 -------check the if this is true by using the two values of gradient as;
-3/2 * 2/3 = - 1 ------ This is true-----equation i
II.
-2x + 3y = -5
3y = 2x -5
y= 2/3 x -5/3 -----m2 here is 2/3
m1*m2 = -1
-3/2 * 2/3 = -1 -----this is true , so ----equation ii
iii)
2x + 3y = 2
3y = -2x + 2
y= -2/3 x + 2/3 -----m2 = -2/3
m1*m2 = -1
-3/2 * -2/3 = 1 -----this is not true,,,equation iii is not perpendicular to our equation.
so, equation i and ii are perpendicular to our equation .
Answer : B i and ii only