Question

helppppp

Answer 1

as an example, here is the method for the first eqinequality:
\(x+2y\ge 6\).
Isolate the variable \(y\):
\(2y\ge 6-x \)
\(y\ge \frac12(6-x) = -\frac{x}2 +3\).

The boundary of the region IS the line whose equation is \(y=-\frac{x}2 +3\)

Answer 2

umm okay :)

Answer 3

to decide if it's the region above or below the line, look at the inequality symbol.
\(y \ge ... \) means it's above. (the inequality means: for some given x, the point (x,y) is in the region if y is bigger than the quantity -x/2+3 who's the point on the line)
\(y\le ... \) means it's below.

Answer 4

the first inequality goes with graph D.

Answer 5

A quick way to decide which side of the line to shade: see if (0,0) makes the inequality true or false. If it is true, shade the side that contains (0,0), otherwise shade the other side. If the inequality is \[x +2y \ge 6\]then plugging in 0 for x and y gives \[0 + 2(0) \ge 6\]which obviously isn't true. That means that the region containing (0,0) is NOT the one to shade.