How do you graph the inequality #x + 2y <=8#, #x>=0# and #y>=0#?

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Answer 1 · 2018-03-06T12:30:33

as in the explanantion

For the blue line: #x+2y<=8#

Write as: #x+2y=8color(red)( larr" For only the line")#

Subtract #x# from both sides

#2y=-x+8#

Divide both sides by 2

#y=-1/2x+4#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(green)("As we are using "<=" the line is solid")#

IFF we had been using #<# the line would be dotted or dashed

So as we have not 'moved' the #y# or multiplied by (-1) the sign #<=# is the same way round in relation to #y# giving:

#y<=-1/2x+4# giving us the acceptably reagion for THIS LINE ALONE.

The other conditions of #x>0 and y>0# means that we can only use the positive region of #y<=-1/2x+4#

Tony B