Question

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

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

I'm thinking the 3rd one.

Answer 2

This boundary line is dashed because the inequality is > rather than ≥. Then, plug in the origin to see if it is a solution. Remember, if the ordered pair makes the inequality true, then it is included.
4x - y > -6
4(0) - (0) > -6
0 > -6
This is true, so the origin is included. Is there a fourth choice?

Answer 3

Their was one more on top but I got it wrong when I chose it the first time. >.<

Answer 4

That's strange. Is there supposed to be a line under the >? Like ≥?

Answer 5

It said included origin but it counted it wrong last time.

Answer 6

Nope. It's -4x - y > -6

Answer 7

Eh nvm >.< Your right.

Answer 8

She flipped the sign the first time I did it.

Answer 9

Do you mind checking another one for me please?

Answer 10

Sure

Answer 11

Determine the type of boundary line and shading for the graph of the inequality y<= 2x + 6

Answer 12

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 13

I think it's the second one.

Answer 14

y ≤ 2x + 6
The boundary line is solid because it is ≤. Did you try the last one?

Answer 15

No. I didn't have the question last time.

Answer 16

I would say it's the last one because you plug in the origin again.
y ≤ 2x + 6
0 ≤ 2(0) + 6
0 ≤ 6
The origin is included.

Answer 17

Thanks (:

Answer 18

Do you understand how to do this stuff though?

Answer 19

A little bit.

Answer 20

Do I just plug in zero?

Answer 21

For the part with the origin yes. If it is true, then the origin is included. If it'f false, then the origin is not included. This is true for any ordered pair. Also, you understand the dashed line and solid line right?

Answer 22

Yes, I know the line.

Answer 23

For instance, if you have to see if (9, 3) is included, plug in 9 for "x" and 3 for "y"