Question

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

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

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

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

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

Answer 1

okay so first...what type of line

dashed means < or >
solid means >= or <=

which do we have? so what type of line do we have?

Answer 2

For <= and >= line will be solid because it's included
For < and > line will be dashed because it's excluded

Answer 3

solid line

Answer 4

nope

Answer 5

so as @nader1 has shown...you will have a solid line

now...does it include the origin?

(plug in the point (0,0)

so

y <= 2x + 4
plug in y = 0 and x = 0

0 <= 2(0) + 4
0<= 0 + 4
0 <= 4

is this true?

yes...so it will be included...

so a solid line...with shading that INCLUDES the origin

Answer 6

You can plug origin (0,0) into equation of a line.
If it's true statement - shade the side with origin.
Otherwise shade opposite side.

Answer 7

@nader1 yes it will be a solid line......the equation is

y <= 2x + 4

<=

Answer 8

isnt Dashed boundary line with shading on the side that includes the origin.? ?

Answer 9

no...just like you stated above...it is a DASHED line....when the equation is < or > because it excludes the point

it is a SOLID line...when it is <= or >= because it includes the point

Answer 10

but are you there is equal i solve for other people without equal that why i am asking

Answer 11

i solve it same probleme but y < 2x + 4

Answer 12

no, you have to remember that equation is NOT the same as

y <= 2x + 4

Answer 13

i know but same problem different with equal but i am asking maybe without equal if with equal ofc solid but i am asking him to be sure if with equal