Determine the type of boundary line and shading for the graph of the inequality -3x - y -6

Question

Determine the type of boundary line and shading for the graph of the inequality -3x - y > -6

anonymous · Answer

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.

anonymous · Answer

this is something similar but also could be usefull for you
Determine the type of boundary line and shading for the graph of the inequality -4x - y >= -8
Answer
		Solid line with shading on the side that includes the origin.
		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.

anonymous · Answer

... that was not helpful at all.

ranga · Answer

Whenever the inequality is just < or > the boundary will be a dashed line Whenever the inequality is just <= or >= the boundary will be a solid line But we need to solve the inequality first to answer the full question.

texaschic101 · Answer

if there is no equal sign, it is a dashed line
if there is an equal sign, it is a solid line

anonymous · Answer

alrighty, i got that :). the part that confuses me is the origin thingy

anonymous · Answer

btw i got y>3x-6  is that right?

texaschic101 · Answer

you need to solve your inequality for y.
-3x - y > -6
-y > 3x - 6 (multiply by -1)
y < -3x + 6
oh....you already got this

ranga · Answer

Here they are interested only in the origin.  All you have to do is plug in x = 0, y = 0 into the inequality and determine whether the origin is on the side of the solution or on the other side.

texaschic101 · Answer

wait....I got y < -3x + 6

anonymous · Answer

okay, so it's a dashed line. would it include or not include the origin?

ranga · Answer

Both of you got the same answer.  Just multiply by -1 and flip the < to > or vice-versa.

ranga · Answer

If I put x = 0, y = 0 in -3x - y > -6
I get 0 > -6  which is true.
Therefore, origin is on the solution side.
We shaded the solution side 
And because the inequality does not include an equal sign the boundary line will be dashed.
So dashed line with shading that included origin.

anonymous · Answer

ohh okay i get it now. Thank you so much : )!!

ranga · Answer

you are welcome.