Question

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

Answer 1

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 `(0, -4)`

For: `x = -4`

`y = -4 - (-4)`

`y = -4 + 4`

`y = 0` or `(-4, 0)`

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]}

Answer 2

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:

`(2 , 2)`

`y> -4-x`

`2> -4-(2)`

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

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