Question

Determine the type of boundary line and shading for the graph of the inequality 4x + y > −6.

Answer 1

ANSWER

Boundary line: dashed line.(not a solid boundary line)

Shading: We shade the upper half-plane.

EXPLANATION

The given inequality is

$4x + y \: > - 6$

To graph this inequality, we graph the corresponding linear equation.

$4x + y \: = \: - 6$

This is what we called the boundary line.

Since the inequality sign does not have an equal sign against, it means the boundary line is not inclusive.

This means that any point on the boundary line will not satisfy the inequality.

So we use a dashed line for the boundary line of this inequality.

We then test to see if the origin satisfies the inequality, because the boundary line is not passing through the origin.

$4(0) + 0 \: > - 6$

$0 \: > - 6$

This statement is true, so we shade the upper half plane.

See graph