This equation is in Standard Linear form. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#

Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)#

#x - y = 6# is:

#color(red)(1)x + color(blue)(-1)y = color(green)(6)#

Therefore the slope is: #m = color(red)(-1)/color(blue)(-1) = 1#

To find the #y# intercept, set #x# to #0# and solve for #y#:

#x - y = 6# becomes:

#0 - y = 6#

#-y = 6#

#color(red)(-1) * -y = color(red)(-1) * 6#

#y = -6#

Therefore, the #y#-intercept is: #-6# or #(0, -6)#

If you also need the #x# intercept, do the opposite. Set #y# to #0# and solve the #x#:

#x - y = 6# becomes:

#x - 0 = 6#

#x = 6#

Therefore, the #x#-intercept is: #6# or #(6, 0)#