Question

Determine the type of boundary line and shading for the graph of the inequality y >= 2x + 4
Answer

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

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

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

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

Answer 1

If you have something in the form y >= mx+b, first graph y=mx+b. This is the boundary line of your shaded region.

Now because the sign is a >= sign, this means we're including the boundary. So the boundary line is a sold line.


Also, since there's a > in the inequality sign, this means we shade above the line y = 2x+4. So you'll be able to tell if (0,0) is in the shaded region or not.

Answer 2

so whats the answer?

Answer 3

Another way to do it is to plug x=0 and y=0 into y >=2x+4 to get 0 >=2(0)+4 which simplifies to 0 > 4


Since that last inequality is NOT true, this means that (0,0) is NOT in the shaded region. So the origin is NOT in the shaded region.

Answer 4

just tell me which one it is

Answer 5

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