Why do we shade a region instead of only drawing the boundary line?

For an x-inequality, shade to the right if x is greater than the boundary value ($x > c$ or $x \ge c$), and shade to the left if x is less than the boundary value ($x < c$ or $x \le c$).

Conditions: The inequality restricts x.; The boundary is a vertical line $x = c$.

To graph $y \le 2$, first draw a horizontal boundary line at $y = 2$. Make the line solid because the inequality includes equality.

Conditions: The inequality restricts only one variable (y).; The inequality is non-strict (≤).

An inequality produces a vertical boundary when it restricts only the x-coordinate (e.g., $x = c$). It produces a horizontal boundary when it restricts only the y-coordinate (e.g., $y = c$).

Conditions: The inequality is in an xy-coordinate system.; The boundary is determined by replacing the inequality with equality.

The boundary line is solid because the inequality includes equality. Since x can be less than or equal to -2, the points on the line $x = -2$ are part of the solution set.

Conditions: The inequality is non-strict (≤).; The boundary line is $x = -2$.

The region above $y = -4$ is shaded because the inequality $y > -4$ requires the y-coordinate to be greater than -4. On a standard coordinate plane, larger y-values are located above the horizontal line $y = -4$.

Conditions: The inequality restricts y.; The boundary is a horizontal line $y = -4$.