The problem asks to graph the inequality $x + y < 1$.

1. Problem Description

The problem asks to graph the inequality $x + y < 1$.

2. Solution Steps

First, we rewrite the inequality in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

$x + y < 1$

Subtract $x$ from both sides:

$y < -x + 1$

The corresponding equation is $y = -x + 1$. This is a line with a slope of $-1$ and a y-intercept of $1$.

Since the inequality is strictly less than, we draw a dashed line to indicate that the points on the line are not included in the solution.

To determine which side of the line to shade, we can test a point that is not on the line. A convenient point is $(0, 0)$.

Substitute $x = 0$ and $y = 0$ into the inequality $x + y < 1$:

$0 + 0 < 1$

$0 < 1$

Since this is true, we shade the region containing the point $(0, 0)$. This is the region below the line.

3. Final Answer

The solution is the region below the dashed line $y = -x + 1$. The line has a y-intercept of 1 and a slope of -

1.