Question

write the system of inequalities shown by the graph. write each inequality in slope-intercept form.

Explanation:

Step1: Find solid line equation

Identify points $(-1,2)$ and $(0,4)$. Slope $m=\frac{4-2}{0-(-1)}=2$. Y-intercept $b=4$. Equation: $y=2x+4$. Shade is above, so inequality: $y\geq 2x+4$

Step2: Find dashed line equation

Identify points $(0,9)$ and $(1,6)$. Slope $m=\frac{6-9}{1-0}=-3$. Y-intercept $b=9$. Equation: $y=-3x+9$. Shade is below, so inequality: $y < -3x+9$

Answer:

$\boldsymbol{y\geq 2x+4}$
$\boldsymbol{y < -3x+9}$