#color(blue)("Consider: "x+y=3)#

Subtract #x# from both sides

#+x+y=3#

#ul(-x color(white)("dddddddd")- x)#

#color(white)("d.")0+y=3-x#

#color(white)("dddddddd")color(red)(ul(bar(|color(white)(2/2)y=-x+3color(white)(2/2)|)))#

The line crosses the x-axis at #y=0 =>0=-x+3 =>x=3#

So we have #x_("intercept")->(x,y)=(3,0)#

The line crosses the y-axis at #x=0=>y=0+3#

So we have #y_("intercept")->(x,y)=(0,3)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Consider: "x-y=1)#

Add #y# to both sides

Subtract 1 from both sides

#x-y color(white)("dddd")=color(white)("dddd")+1#

#ul(color(white)(x)+y-1color(white)("dddd")+y-1)#

#x+0-1color(white)("d") =color(white)("ddd") y+0#

#color(white)("dddddddd")color(red)(ul(bar(|color(white)(2/2)y=x-1color(white)(2/2)|)))#

The line crosses the x-axis at #y=0=> 0=x-1 =>x=1#

So we have #x_("intercept")->(x,y)=(1,0)#

The line crosses the y-axis at #x=0=>y=0-1#

So we have #y_("intercept")->(x,y)=(0,-1)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~