Give the inequalities for (x, y) that determine the unshaded regions in the following:

The unshaded region is bounded by the line $y=0$ from below and $y=3$ from above.

The region below $y=0$ is shaded, meaning $y \geq 0$ is unshaded.
The region above $y=3$ is shaded, meaning $y \leq 3$ is unshaded.
Combining these, the unshaded region is between $y=0$ and $y=3$, inclusive.

The unshaded region is bounded by the line $x=-2$ from the left and $x=2$ from the right.

The region to the left of $x=-2$ is shaded, meaning $x \geq -2$ is unshaded.
The region to the right of $x=2$ is shaded, meaning $x \leq 2$ is unshaded.
Combining these, the unshaded region is between $x=-2$ and $x=2$, inclusive.

The line passes through $(0,0)$, $(1,1)$, $(2,2)$, which is the line $y=x$.

The region below the line $y=x$ is shaded. This means the unshaded region is above or on the line $y=x$.

The line passes through $(-3,3)$, $(0,0)$, $(3,-3)$. The slope is $\frac{0-3}{0-(-3)} = \frac{-3}{3} = -1$. The y-intercept is 0. So the equation of the line is $y=-x$.

The region above the line $y=-x$ is shaded. This means the unshaded region is below or on the line $y=-x$.