write the given equation in a standard form
3x + 4y = 6
4y = 6 - 3x
4y = - 3x + 6
divided by 4 in both sides
y = - 4/3x + 3/2
standard form of a linear equation is
y = mx +c
therefore m for gradient is -4/3
the product of the gradient of the lines that are perpendicular to each other is -1
- 4/3 × mx = -1
mx = 3/4
y = mx + c
-5 = 3/4(2) + c
-5 = 3/2 + c
c = -13/2
therefore your equation is
y = 3/4x - 13/2
