Question

Determine the type of boundary line and shading for the graph of the inequality 4x + y > -6.

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

I graphed it and it came out like this: http://prntscr.com/449exe

Answer 2

So its either A or C

Answer 3

yes \(\gt \) or \(\lt\) give you dashed line
where as \(\ge\) or \(\le \) gives you solid line

Answer 4

Oh ok and what does it mean by origin? ik the orgin of a coordinate plane is (0,0) i think...

Answer 5

Very good :) to know whether the shaded region contains the origin or not, plugin `x=0`, and ` y=0` in the inequality and check if it satisfies

Answer 6

Oh ok Thank you!

Answer 7

nice job ganeshie :)

Answer 8

4x + y > -6

4(0) + 0 > -6

0 > -6

Clearly, 0 is greater than ANY negative number as 0 lies on right side of all negative numbers on number line. So the shaded region contains the origin.

Answer 9

:) you may see this in your graph as well, the intersection of x and y axes is called origin, and you can see that the shaded region includes that intersection

Answer 10

oh ok so if (0,0) is in the shaded region the inequlity contains the origin?

Answer 11

Yep !

Answer 12

Thank You!

Answer 13

yw :)