the type of boundary line and shading for the graph of the inequality -2x - y >= -8

Question

 y = 2x + 8

 I know it's going to be above the line and it is going to be dashed, but I don't know how to find the origin. Does it included the origin or does not include the origin?

Answer 1

You are given -2x-y>=-8 Rewrite it as y<=-2x+8 (Move y to the right and -8 to the left). Then the boundary line is straight line given by the equation y=-2x+8 and the region corresponding to the solution is underneath this straight line, that is below the boundary line.

Answer 2

You can always test it by plugging in the origin (0,0) into the original equation to see if it's valid:

-2(0) - (0) >= -8

0 >= -8   <=== true statement

So the origin would be within the shaded region.