Question

help please
Determine the type of boundary line and shading for the graph of the inequality -4x - y less than or greater to -2

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

Hint: when x=0 and y=0, is -4x-y<>2 true or false (you did mean "less than or greater to" and NOT "less than or equal to", right?)

Answer 2

no I meant less than or equal to

Answer 3

do you have your answer?

Answer 4

no I don't can you please help me :(

Answer 5

"-4x-y [sign] -2"
([sign] can be <,>,≥,≤)

what changes between < and ≤ is only the type of border. A '<' means that you cannot have equality between both sides. A '≤' means both sides are allowed to be equal. Therefore, when you use < or >, the boundery line will be dashed, if it's ≤ or ≥, the boundary is a solid line.

Answer 6

This means that if you know how to make a correct drawing with, for example, the inequality sign '≥', then you can find the 3 others very easily.
ok until here?

Answer 7

yes that helps a lot, thanks!

Answer 8

We only look at "-4x - y ≥ -2" right now.
The equation "-4x-y = -2" (equality) is that of a line, this line divides the plane onto two parts.
All you have to do is to pick a point (you choose it) and check if it verifies the inequality.
-If the inequality is ok, that means the point is in the shaded half. (so, the part that contains that point is the correct one..)
-If the inequality is not ok, the shaded region is on the other side of the line.
It is easy to check this for the point (0,0) (unlikely to make errors)

Answer 9

into*

Answer 10

oh oops. in your question it's actually "≤". Fine, the inequality is -4x-y≤2.
- we know it's a solid line.
- check if the origin verifies this inequality
what is the answer ? (a,b,c, or d ?)

Answer 11

B?

Answer 12

you're right. :)

Answer 13

thank you:)