inverse functions

Question

what is the inverse equation for

y=-3/4x+5

Answer 1

y=-(3/4)x +5

switch x and y and solve for the new y to get the inverse function

x =-3y/4 +5

4x =-3y +20

3y = -4x+20

y = (-4x+20)/3

f^-1(x) = -4x/3 + 20/3

However, the way you've written the problem it's equivalent to

y=-3/4x +5

y=-3/(4x) +5

if that's what you intended then for the inverse

x=-3/(4y) + 5

x-5 = -3/(4y)

4y = -3/(x-5)

y = f^-1(x) = -3/(4x-20)

another possible way you might have intended to write is

y= -3/(4x+5), if so, then for the inverse

x=-3/(4y+5)

4y+5 =-3/x

4y = -3/x -5= (-3-5x)/x

y = f^-1(x) = -(3+5x)/4x

technically the 2nd way is how you wrote it

odds are the 1st way is what you intended

but there is some ambiguity in the problem