Question

choose the correct inequality for this graph.
$y < 3x + 1$
$y \geq \frac{1}{3}x - 1$
$y > \frac{1}{3}x - 1$
$y \leq 3x + 1$

Explanation:

Step1: Find line equation

The line has slope $\frac{1}{3}$ and y-intercept $-1$, so equation is $y=\frac{1}{3}x-1$.

Step2: Check line style

Dashed line means $<$ or $>$, not $\leq$ or $\geq$.

Step3: Test shaded region

Test point $(0,0)$: $\frac{1}{3}(0)-1=-1$, $0 > -1$, so inequality is $y > \frac{1}{3}x - 1$.

Answer:

$y > \frac{1}{3}x - 1$