Question

which linear inequality is represented by the graph? $y > \frac{2}{3}x + 3$ $y < \frac{3}{2}x + 3$ $y > \frac{3}{2}x + 3$

Explanation:

Step1: Find slope of the line

Use points $(0,3)$ and $(-5,0)$:
$$m=\frac{0-3}{-5-0}=\frac{3}{5}? \text{No, correct points: } (0,3) \text{ and } (2,6)$$
$$m=\frac{6-3}{2-0}=\frac{3}{2}$$

Step2: Identify y-intercept

The line crosses y-axis at $(0,3)$, so $b=3$. Line equation: $y=\frac{3}{2}x+3$

Step3: Determine inequality sign

Dashed line means $<$ or $>$. Test point $(0,0)$: $0 < \frac{3}{2}(0)+3$ is true, and $(0,0)$ is below the line, so $y < \frac{3}{2}x+3$

Answer:

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