Question

which linear inequality is graphed with ( y > -x - 2 ) to create the given solution set?
( \bigcirc y > x + 1 )
( \bigcirc y < x - 1 )
( \bigcirc y > x - 1 )
( \bigcirc y < x + 1 )

Explanation:

Step1: Identify the second boundary line

The dashed line passes through points $(-1,0)$ and $(0,1)$. Calculate its slope:
$\text{slope} = \frac{1-0}{0-(-1)} = 1$
Using the y-intercept $(0,1)$, the line equation is $y = x + 1$.

Step2: Determine the inequality direction

The shaded region (overlap with $y > -x -2$) is below this line. Since the line is dashed, the inequality is $y < x + 1$.

Answer:

D. $y < x + 1$