# How do you graph y> -4-x on the coordinate plane?

Jan 5, 2018

See a solution process below:

#### Explanation:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: $x = 0$

$y = - 4 - 0$

$y = - 4$ or $\left(0 , - 4\right)$

For: $x = - 4$

$y = - 4 - \left(- 4\right)$

$y = - 4 + 4$

$y = 0$ or $\left(- 4 , 0\right)$

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y+4)^2-0.125)((x+4)^2+y^2-0.125)(y+x+4)=0 [-20, 20, -10, 10]}

We can now change the boundary line to a dashed line because the inequality operator does not contain an "or equal to" clause. And, we can shade the right side of the line.

graph{(y+x+4) > 0 [-20, 20, -10, 10]}

Jan 5, 2018

See below.

#### Explanation:

First graph the line $y = - x - 4$. This will give you the boundary between the included and excluded regions. Remember to use a dashed line as this is a greater than and not a greater than or equal inequality, so the line will not be an included region.

With line plotted, check a set of coordinates above and below the line to see which satisfy the inequality.

graph{y=-x-1 [-10, 10, -5, 5]}

Above the line:

$\left(2 , 2\right)$

$y > - 4 - x$

$2 > - 4 - \left(2\right)$

$2 > - 6 \textcolor{w h i t e}{88}$ TRUE

Area above the line is the included region. Shade this region.

graph{y > -4-x [-41.1, 41.07, -20.55, 20.55]}