Question

$x > -4$
$y < 2x + 4$
select a line to change it between solid and dotted. select a region to shade it.

Explanation:

Step1: Graph $x > -4$

Draw a vertical dotted line at $x=-4$ (since the inequality is strict, not inclusive). Shade all regions to the right of this line, as $x$ values are greater than -4.

Step2: Graph $y < 2x + 4$

First, plot the line $y=2x+4$: it has a y-intercept at $(0,4)$ and a slope of 2 (so another point is $(1,6)$ or $(-2,0)$). Draw this as a dotted line (strict inequality, not inclusive). Shade the region below this line, as $y$ values are less than $2x+4$.

Step3: Identify overlapping region

The solution is the area that is shaded by both inequalities: to the right of $x=-4$ and below $y=2x+4$.

Answer:

1. For $x > -4$: Dotted vertical line at $x=-4$, shade right of the line.
2. For $y < 2x + 4$: Dotted line through $(0,4)$ and $(-2,0)$, shade below the line.
3. The final shaded solution is the overlapping region (right of $x=-4$ and below $y=2x+4$).