How do you graph the system of linear inequalities $2 x + y < 6$ $2x+y<6$ and $y > - 2$ $y> -2$ ?

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How do you graph the system of linear inequalities $2 x + y < 6$ $2x+y<6$ and $y > - 2$ $y> -2$ ?

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Answer 1 · 2015-04-22T13:14:07

$2 x + y < 6$ $2x+y<6$ and $y > - 2$ $y > -2$
First consider the related linear equations:
$2 x + y = 6 \to y = - 2 x + 6$ $2x+y=6 rarr y = -2x+6$
and
$y = - 2$ $y = -2$

$y = - 2 x + 6$ $y = -2x+6$
is a line with y-intercept at $(0, 6)$ $(0,6)$ and a slope of $(- 2)$ $(-2)$ (which means that for every unit increase in $x$ $x$ , $y$ $y$ decreases by $2$ $2$ )

$y = - 2$ $y=-2$
is a horizontal line through the point $(0, - 2)$ $(0,-2)$

It is fairly simple to plot these lines;
then we just need to determine which sides of these lines need to be combined for the given inequalities
Since
$y ≻ 2$ $y>-2$
the points of the Range must be above the horizontal line

Since
$2 x + y < 6$ $2x+y<6$
the points of the Range must be below the line for $2 x + y = 6$ $2x+y=6$ (since if $y_{1}$ $y_1$ is in the Range and $y_{2} < y_{1}$ $y_2<y_1$ then $y_{2}$ $y_2$ must also be in the Range).
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How do you graph the system of linear inequalities $2 x + y < 6$ $2x+y<6$ and $y > - 2$ $y> -2$ ?

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