Slope intercept form of equation of a line is

#y=mx+c#, where #m# is its slope and #c# is its intercept on #y#-axis

So if you want to know slope of a line and its intercept n #x#-axis, just express #y# in terms of #x# and coefficient of #x# will be the slope and any constant term added to it will be its intercept on #y# axis.

As we have #x-y=10#, this means #x-y+y=10+y#

or #x=10+y# i.e. #10+y=x# and hence

#10+y-10=x-10#

or #y=x-10# i.e. the form which we desired

Now as coefficient of #x# is #1#, slope of line #1#

and as constant term is #-10#, #y#-intercept is #-10#

In case you want #x# intercept, just put #y=0# in the equation

#x-y=10# and we get #x-0=10# or #x=10#

Hence #x#-intercept is #10#

graph{x-10 [-20.33, 19.67, -14.8, 5.2]}