#f(x)=3x-8# is the equation of a line in slope-intercept form with a slope of #3#.

All lines parallel to #f(x)=3x-8# have the same slope.

Temporarily, writing #y# in place of #f(x)# :

the equation of a line through #(hatx,haty)=(5,8)# with a slope of #m=3# can be written in point slope form as:

#color(white)("XXXX")##(y-haty)= m(x-hatx)#

or

#color(white)("XXXX")##(y-8) = 3(x-5)#

We can simplify this:

multiplying through the right side:

#color(white)("XXXX")##y-8 = 3x-15#

subtracting #y# from both sides:

#color(white)("X8XXX")##-8 = 3x -15 -y#

adding #15# to both sides

#color(white)("XXXX")##7 = 3x-y#

Or, going back to #y-8=3x-15# and restoring #f(x)# for #y#:

#color(white)("XXXX")##f(x)-8 = 3x-15#

#color(white)("XXXX")##f(x)= 3x-7#