Question

Determine the type of boundary line and shading for the graph of the inequality -4x - y -2

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

Where the inequality symbol?

Answer 2

after the y

Answer 3

< =

Answer 4

≤

Answer 5

yes

Answer 6

-4x - y ≤ -2

Answer 7

yes

Answer 8

For these, you have to isolate y:
4x - y ≤ -2
4x + 2 ≤ y

Answer 9

okay

Answer 10

Do you know how to read the expression?

Answer 11

no i don't

Answer 12

Well, it means that y is greater than or equal to four times x plus two.

Answer 13

okay how do i tell if it is dashed or solid? and the shading?

Answer 14

If the inequality has ≤ or ≥, then the end line of the shading will be solid.
If the inequality has < or >, then the end line of the shading will be dashed.

Answer 15

ohh okay.

Answer 16

< means less than
> means greater than
≤ means less than or equal
≥ means greater than or equal

Answer 17

Solid line with shading on the side that does not include the origin. is this correct?

Answer 18

How do you know the origin is not included?

Answer 19

well you told me that it is a solid line and i just guessed that it wasn't included

Answer 20

No, you do not guess. To figure out if the origin is included, you have to make sure y is isolated. Then plug in the point (0,0). If it is true, then the point is included. If it is false, then the point is not included.

Answer 21

4x + 2 ≤ y
4(0) + 2 ≤ 0
2 ≤ 0 False

That's how you know the origin is not included.