Explanation:
the line equation
y = ax + b
gives us slope (a) and y-interception (b).
4x + 3y = 5
3y = -4x + 5
y = -4/3 × x + 5/3
the slope of the original line is therefore -4/3.
a perpendicular slope flips x and y upside-down and flips the sign.
so, the perpendicular slope of -4/3 is 3/4.
the desired line looks like
y = 3/4 × x + b
b we get by using the given point and its coordinates :
-3 = 3/4 × 3 + b = 9/4 + b
-12/4 = 9/4 + b
b = -21/4
so our full line equation is
y = 3/4 × x - 21/4
or
4y = 3x - 21
-3x + 4y = -21