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

Apr 22, 2015

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

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

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

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
$y \succ 2$
the points of the Range must be above the horizontal line

Since
$2 x + y < 6$
the points of the Range must be below the line for $2 x + y = 6$ (since if ${y}_{1}$ is in the Range and ${y}_{2} < {y}_{1}$ then ${y}_{2}$ must also be in the Range).