Question

Help!! Determine the type of boundary line and shading for the graph of the inequality y greater than or equal to 2x + 4

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

there is a rule for the boundary line
if it is < or > use a dashed line
if it is ≤ or ≥ use a solid line (use the underline to remember solid)

Answer 2

i know its a dashed line

Answer 3

i just dont know if its the Dashed line with shading on the side that includes the origin.or Dashed line with shading on the side that does not include the origin.

Answer 4

you have
y ≥ 2x + 4

that is a greater than or equal. Are you sure it is dashed ?

Answer 5

i think so ? cause isnt if its equal its dashed??

Answer 6

the "equal part" makes it solid
see http://www.regentsprep.org/Regents/math/ALGEBRA/AE85/GrIneqa.htm
point #3

Answer 7

o

Answer 8

so the second one??

Answer 9

next, for your problem
y ≥ 2x + 4

where is (0,0) ? in the shaded region or not ?
to find out, replace x with 0 and replace y with 0

0 ≥ ? 2*0+4
0 ≥ 0+4
0≥ 4

is 0 greater than or equal to 4 ?
no.
so (0,0) is in the "unshaded part"

Answer 10

we shade the area that is "true" where y is greater than or equal to the line

Answer 11

if we replace x and y with 0,0 in
y ≥ 2x + 4

will it show y greater than the right hand side ?

Answer 12

you do not have to guess. you replace x and y with 0 and get
0 ≥ 2*0+4

is that true ?

Answer 13

do you know that
2*0+4 is 4 ?

Answer 14

so the question is 0 ≥ 4
is 0 bigger than 4 ?
would you rather have 0 dollars or 4 dollars ?

anyway, it is not true. the origin (0,0) is a point where y < 2x+4 (below the line, in the unshaded area)