Question

: standard form date lity. 2) ( x + y leq 1 )

Explanation:

Step1: Rewrite to slope-intercept form

Rearrange $x+y\leq1$ to $y\leq -x + 1$

Step2: Identify boundary line

The boundary is $y=-x+1$ (solid line, since $\leq$ includes equality).
Find intercepts:

• When $x=0$, $y=1$ (y-intercept: $(0,1)$)
• When $y=0$, $x=1$ (x-intercept: $(1,0)$)

Step3: Test a point for shading

Use $(0,0)$: $0+0\leq1$ is true. Shade the region containing $(0,0)$ (below/left of the line).

Answer:

1. Draw a solid line connecting the points $(0,1)$ and $(1,0)$.
2. Shade the entire region that lies below and to the left of this line (including the line itself).