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

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