Question

□ $y\ge -0.5x + 4$
□ $3x + y < 2$
□ $x + 3y < 4$
□ $x + 3y \le 4$
□ $y > -3x + 2$
□ $3x + y \le 2$

Explanation:

Step1: Identify line from intercepts

The dashed line passes through $(0, 2)$ and $(1, -1)$. Calculate slope:
$m=\frac{-1-2}{1-0}=-3$
Equation: $y=-3x+2$

Step2: Test region inequality

Pick test point $(0,0)$ (shaded region):
$0 > -3(0)+2$? No. $0 < -3(0)+2$? Yes. The line is dashed, so use $<$. Rewrite $y < -3x+2$ as $3x+y < 2$.

Step3: Verify boundary type

Dashed line means strict inequality ($<$), so exclude $\leq$ options.

Answer:

$\boldsymbol{3x+y < 2}$