Respuesta :
Answer:
The correct option is A.
Step-by-step explanation:
The given inequality is
[tex]y\leq -2x[/tex]
The sign of inequality is ≤, it means the points on relation line lie in the solution set.
The related equation of the inequality is
[tex]y=-2x[/tex]
At x=0,
[tex]y=-2(0)=0[/tex]
At x=1,
[tex]y=-2(1)=-2[/tex]
Plot the points (0,0) and (1,-2) on a coordinate plane.
The sign of inequality is ≤, it means we have shade below the line.
The point (-2,4) and (3,-6) are in solution set because,
[tex]4\leq -2(2)\Rightarrow 4\leq 4[/tex] (True)
[tex]-6\leq -2(3)\Rightarrow -6\leq -6[/tex] (True)
Therefore option A is correct.
The points (1,2) and (1,3) are not in the solution set because,
[tex]2\leq -2(1)\Rightarrow 2\leq -2[/tex] (False)
[tex]3\leq -2(1)\Rightarrow 3\leq -2[/tex] (False)
Therefore options B,C and D are incorrect.
