Question

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

Dashed line with shading on the side that includes the origin.

Solid line with shading on the side that does not include the origin.

Dashed line with shading on the side that does not include the origin.

Solid line with shading on the side that includes the origin.

Answer 1

First, you want to solve the equation for y.
You can do that by subtracting 4x from both sides.
That gives you y > -6 - 4x.
The boundary line is dashed if the boundary is not part of the solution, so the inequality uses the operator < or >. We know that the line is dashed. That narrows it down to either the 1st or 3rd option.
In order to see if the shading includes the origin (0,0) we need to plug it into the equation for x and y, like
0 > -6 - 4(0)
0 > -6 - 0
0 > -6
Since 0 > -6 is a true statement, we know that (0,0) is a solution. Shade the half-plane that contains the origin.
So your answer would be the 1st answer, dashed line with shading on the side that includes the origin. Does that make sense?

Answer 2

omg yes , thank you so much

Answer 3

You're welcome :D