Determine the type of boundary line and shading for the graph of the inequality -2x - y < -6
Choose one answer.
a. Dashed line with shading on the side that includes the origin.
b. Solid line with shading on the side that does not include the origin.
c. Dashed line with shading on the side that does not include the origin.
d. Solid line with shading on the side that includes the origin.

- anonymous

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- anonymous

so it is less than which means dashed?

- DanJS

put in the form y > .... first

- anonymous

oh alright

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## More answers

- DanJS

y > -2x + 6

- anonymous

dashed still?

- DanJS

yes,
\[\gt~or ~\lt~~dashed\]
\[\ge~or~\le~~solid line\]

- DanJS

just remember it can equal the line, so solid line means include those points on the line

- anonymous

oh alright

- DanJS

now you can just pick 2 points and connect them, x=0 and x=1

- DanJS

When x=0, y = 6, point (x,y) = (0,6)
When X=1, y = -2 + 6 = 4 . point (x,y) = (1,4)

- anonymous

this does not include the origin
correct?

- DanJS

|dw:1437601290059:dw|

- anonymous

http://gyazo.com/9ad5ae8bf49066d458c9301d46619cf4

- DanJS

Since it is "Less than" you shade underneath the line...

- DanJS

Greater than, you would shade above

- anonymous

so above

- anonymous

you said earlier the equation was different. i showed it in my link

- DanJS

yeah i just noticed i mistyped,... right y > -2x + 6 , greater than , shade above the line

- anonymous

are you sure its dashed line for greater than or less than?

- anonymous

i would think it would be solid in that case

- DanJS

yes
greater than or less than, dashed line, it doesnt include the line,

- anonymous

so the answer to this one was c

- DanJS

yes, another quick thing you could do for these types probs, is simply test the origin

- DanJS

x = 0, y = 0
-2*0 - 0 < - 6
0 < 6 False, the origin is not part of the solution/shaded area

- DanJS

and it is dotted because of > or <

- anonymous

could i check another equation?

- DanJS

sure, we can do it the quick way

- anonymous

just wanna make sure im doing it right i got the answer already i think

- anonymous

http://gyazo.com/f91fa996a6ecec7fd818376c3715b8ec

- anonymous

a. 2x - 5y -10
b. x - y > 3
c. 2x - y < -4
d. x + 2y -8

- anonymous

i chose d

- DanJS

what is the sign in d

- anonymous

greater than or equal to

- DanJS

ok, that part is right, it is a solid line and shaded above > or = to

- DanJS

now test a couple points on the line...
When x =0, y=-4 on the graph, test in answer d

- DanJS

0 + 2y = -8
y = -4 , so far so good, now test one more point

- DanJS

When y=0, x = -8 on the graph..
x + 2(0) = -8
True also,
choice d works

- anonymous

Alright
thanks for the help

- DanJS

no prob, good luck

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