Question

which linear inequality is represented by the graph?

• ( y leq 2x + 4 )
• ( y leq \frac{1}{2}x + 3 )
• ( y geq \frac{1}{2}x + 3 )
• ( y geq 2x + 3 )

Explanation:

Step1: Find line slope

Use points $(-6,0)$ and $(0,3)$:
$$m=\frac{3-0}{0-(-6)}=\frac{3}{6}=\frac{1}{2}$$

Step2: Find line equation

Y-intercept $b=3$, so:
$$y=\frac{1}{2}x+3$$

Step3: Determine inequality sign

Shaded area is above solid line, so use $\geq$.

Answer:

$\boldsymbol{y \geq \frac{1}{2}x + 3}$ (Option C)