To find the slope and y-intercept of this equation we must transform it into the slope-intercept form.

The slope-intercept form of a linear equation is:

#y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b# is the y-intercept value.

We can solve this equation for #y# to transform the equation we have been given in this problem into this form:

#9x - 3y = 81#

#9x - color(red)(9x) - 3y = color(red)(-9x) + 81#

#0 - 3y = color(red)(-9x) + 81#

#-3y = - color(red)(-9x) + 81#

#(-3y)/color(green)(-3) = (color(red)(-9x) + 81)/color(green)(-3)#

#(color(green)(cancel(color(black)(-3)))y)/cancel(color(green)(-3)) = (color(red)(-9x) + 81)/color(green)(-3)#

#y = (color(red)(-9x) + 81)/color(green)(-3)#

#y = color(red)(-9x)/color(green)(-3) + 81/color(green)(-3)#

#y = 3x - 27#

Therefore the slope is #color(red)(3)# and the y-intercept is #color(blue)(-27)# or (#color(blue)(0, -27)#)