It takes quite a bit of practice but once you are used to these #ul("some of them")# you do not need to do any manipulation on paper to find the values. As you get better and better you can do more and more of them in your mind.
Changing this to the form of #y=mx+c# where #m# is the slope and #c# is the y-intercept
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Given: #-3x+8y=16#
First we isolate the term with the #y#. In that we move the #-3x# to the other side of the =.
Add #color(red)(3x)# to both sides
#color(green)(-3x+8y=16color(white)("ddd") ->color(white)("ddd")-3x color(red)(+3x)+8y=16 color(red)(+3x))#
#color(white)("ddddddddddddddd")->color(white)("dddddddd")color(green)(0color(white)("dd")+8y=3x+16)#
Now we 'get' #y# on its own. In that we move the 8 to the other side of the =.
Multiply everything in each side by #color(red)(1/8)#
#color(green)(8y=3x+16color(white)("ddd")->color(white)("ddd")8/color(red)(8)y=3/color(red)(8)x+16/color(red)(8)#
# color(white)("ddddddddddddd")->color(green)(color(white)("ddd")1xxy=3/8x+2)#
#color(green)(color(white)("ddddddddddddd")->color(white)("ddd")y=3/8x+2)#
Slope is #+3/8 and y_("intercept")=+2#
