Question

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

@satellite73 @amistre64 ?

Answer 2

@mathslover @dmezzullo

Answer 3

I got this

Answer 4

Okay.

Answer 5

first look at the sign for your inequality

Answer 6

It's a solid line right? I just don't know if it's with or without origin.

Answer 7

it is > which is greater than
it doesn't include values that are on the line, just the values above the line
so we represent this as a dashed line

Answer 8

you see?

Answer 9

Oh, okay.

Answer 10

and then for the other part, what's the basic form of a line?

Answer 11

y=...

Answer 12

@unheard you there?

Answer 13

y = mx + b?

Answer 14

yes. so what is b?

Answer 15

and what value of b must a line have to pass through the origin?

Answer 16

b is 6

Answer 17

do you go to an online school?

Answer 18

for a line to pass through the origin it must have b=0. For the inequality to include the origin, b would have to be less than zero.

Answer 19

So, it does not include the origin.

Answer 20

yes

Answer 21

Awesome, Thanks.

Answer 22

now the real question is, can you do it again?

Answer 23

It is A, but it's important that you see why.
When you plug 0 in for x, you see that the inequality is y < 6. Since the origin (0) is less than 6, it is included in the solution. So you are shading the region that includes the origin.

Answer 24

y<4x+1

Answer 25

same question

Answer 26

haha

Answer 27

and also\[y \ge 3x-1\]

Answer 28

Ohh okay