How do you graph $x - 4 y \geq - 8$ $x-4y>=-8$ ?

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How do you graph $x - 4 y \geq - 8$ $x-4y>=-8$ ?

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Answer 1 · 2016-07-16T10:34:41

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Explanation:

$Making the y term positive$ $color(brown)("Making the "y" term positive")$

Multiply by (-1)

$- x + 4 y \leq - 8 \leftarrow notice that the \geq is now \leq$ $-x+4y<=-8" "larr" notice that the ">=" is now "<=$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Isolate the y term$ $color(brown)("Isolate the "y" term")$

Add $x$ $x$ to both sides

$- x + x + 4 y \leq - 8 + x$ $-x+x+4y<=-8+x$

$4 y \leq x - 8$ $4y<=x-8$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Isolate the y$ $color(brown)("Isolate the "y)$

Divide both sides by 4

$\frac{4}{4} \times y \leq \frac{x}{4} - \frac{8}{4}$ $4/4xx y<=x/4-8/4$

$y \leq \frac{x}{4} - 2$ $y<=x/4-2$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Now plot your graph the normal way$ $color(brown)("Now plot your graph the normal way")$

At $y = 0 \to x = 8$ $y=0 -> x=8$
At $x = 0 \to y = - 2$ $x=0-> y=-2$
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How do you graph $x - 4 y \geq - 8$ $x-4y>=-8$ ?

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