To find the x-intercept we set #color(red)(y)# to #color(red)(0)# and solve for #x#:

#8color(red)(y) - 5 = 3x# becomes:

#(8 xx color(red)(0)) - 5 = 3x#

#0 - 5 = 3x#

#-5 = 3x#

#-5/color(red)(3) = (3x)/color(red)(3)#

#-5/3 = x#

#x = -5/3#

To find the y-intercept we set #color(red)(x)# to #color(red)(0)# and solve for #y#:

#8y - 5 = 3color(red)(x)# becomes:

#8y - 5 = (3 xx color(red)(0))#

#8y - 5 = 0#

#8y - 5 + color(red)(5) = 0 + color(red)(5)#

#8y - 0 = 5#

#(8y)/color(red)(8) = 5/color(red)(8)#

#(color(red)(cancel(color(black)(8)))y)/cancel(color(red)(8)) = 5/8#

#y = 5/8#

The x-intercept is #-5/3# or #(-5/3, 0)#

The y-intercept is #5/8# or #(0, 5/8)#