Question

choose the correct inequality for this graph.
$y \leq \frac{3}{2}x + 1$
$y \leq \frac{2}{3}x + 1$
$y < \frac{2}{3}x + 1$
$y < \frac{3}{2}x + 1$

Explanation:

Step1: Find line slope

Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-1)}{0-(-3)}=\frac{2}{3}$

Step2: Identify y-intercept

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

Step3: Check line style

Solid line means $\leq$ or $\geq$

Step4: Test shaded region

Test $(0,0)$: $0 \leq \frac{2}{3}(0)+1 \to 0 \leq 1$, true. So inequality is $y \leq \frac{2}{3}x+1$

Answer:

B. $y \leq \frac{2}{3}x + 1$