To find the intercepts you need to set the other variable to #0# and solve for the intercept variable you are looking for:
Solution for y-intercept - set #x = 0# and solve for #y#:
#(-31 xx 0) - 4y = 9#
#0 - 4y = 9#
#-4y = 9#
#(-4y)/color(red)(-4) = 9/color(red)(-4)#
#(color(red)(cancel(color(black)(-4)))y)/cancel(color(red)(-4)) = -9/4#
#y = -9/4#; y-intercept is #-9/4# or #(0. -9/4)#
Solution for x-intercept - set #y = 0# and solve for #x#:
#-31x - (4 xx 0) = 9#
#-31x - 0 = 9#
#-31x = 9#
#(-31x)/color(red)(-31) = 9/color(red)(-31)#
#(color(red)(cancel(color(black)(-31)))x)/cancel(color(red)(-31)) = -9/31#
#x = -9/31#; x-intercept is #-9/31# or #(-9/31, 0)#
