How do you find the inverse of #y = (-1/2)x + 7#?

1 Answer

#y^-1=2x-14#

Explanation:

To find the inverse of an equation, we switch #x# and #y#:
#x=(-1/2)y+7#

And solve for #y#:
#xcolor(white)(0000)=(-1/2)y+7#
#ul(color(white)(00)-7color(white)(=(-1/2))-7#
#x-7=(-1/2)y#
#ul(xx2color(white)(=()yyyy)xx2#
#2(x-7)=y#

#y=2x-14#

To write that this equation is the inverse of the original one, we write the expression as #y^-1=2x-14#