Answer:
[tex]y\le\dfrac{1}{2}x+2[/tex]
Step-by-step explanation:
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). This line has the equation
[tex]y-0=\dfrac{2-0}{0-(-4)}(x-(-4))\\ \\y=\dfrac{1}{2}(x+4)\\ \\y=\dfrac{1}{2}x+2[/tex]
The origin belongs to the shaded region, so its coordinates must satisfy the inequality. Since
[tex]\dfrac{1}{2}\cdot 0+2=2\ge 0,[/tex]
then the correct inequality is
[tex]y\le\dfrac{1}{2}x+2[/tex]
