Question

graph the inequality ( x + y < -1 ).

Explanation:

Step1: Rewrite to slope-intercept form

Rearrange the inequality to solve for $y$:
$y < -x - 1$

Step2: Identify boundary line

The boundary is the line $y = -x - 1$. Since the inequality is $<$ (not $\leq$), use a dashed line.

Step3: Test a point for shading

Use the origin $(0,0)$:
$0 + 0 < -1$ simplifies to $0 < -1$, which is false. Shade the half-plane that does NOT contain the origin.

Answer:

1. Draw a dashed line representing $y = -x - 1$ (this line has a y-intercept at $(0, -1)$ and a slope of $-1$).
2. Shade the region below and to the left of this dashed line (all points where $x + y < -1$).