Question

page 283)

1. $y \leq -3x + 1$

$y > -2$

Explanation:

Step1: Graph boundary $y=-3x+1$

This is a line with slope $-3$ and y-intercept $(0,1)$. Since the inequality is $y \leq -3x+1$, draw a solid line, and shade the region below the line.

Step2: Graph boundary $y=-2$

This is a horizontal line. Since the inequality is $y > -2$, draw a dashed line, and shade the region above this line.

Step3: Identify overlapping region

The solution is the area that is shaded by both inequalities: above the dashed line $y=-2$ and below/on the solid line $y=-3x+1$.

Answer:

The solution is the overlapping shaded region: all points that lie above the dashed horizontal line $y=-2$ and on or below the solid line $y=-3x+1$.

To verify key intersection: solve $-2 = -3x + 1$
$3x = 3$
$x=1$
So the boundary intersection point is $(1, -2)$.