Question

write a linear inequality that represents each graph.
32.
33.
34.

Explanation:

Step1: Find line eq for Q32

The line passes through $(0,3)$ and $(2,0)$. Slope $m=\frac{0-3}{2-0}=-\frac{3}{2}$. Equation: $y=-\frac{3}{2}x+3$, or $3x+2y=6$. Solid line, shaded above: $\boldsymbol{3x+2y\geq6}$

Step2: Find line eq for Q33

The line passes through $(0,-2)$ and $(3,1)$. Slope $m=\frac{1-(-2)}{3-0}=1$. Equation: $y=x-2$, or $x-y=2$. Dashed line, shaded below: $\boldsymbol{x-y>2}$

Step3: Find line eq for Q34

Vertical line at $x=3$. Dashed line, shaded right: $\boldsymbol{x>3}$

Answer:

1. $3x+2y\geq6$
2. $x-y>2$
3. $x>3$