Answer:
Option C is the correct choice that is [tex]y<-\frac{5}{2}x-2[/tex]
Step-by-step explanation:
As this is a multiple choice question we will reduce the options and work on it with the given points [tex](0,-2),(-2,-3)[/tex]
Note:We know that [tex]\leq ,\geq[/tex] where there is [tex]=[/tex] sign associated with it have a straight line graph there is no breaking in the line.
And when there is simply [tex]<,>[/tex] we have a dashed line when we plot it on a graph.
So option B and D are discarded.
Now one-by one we will put the values [tex](x,y)\ (-2,3)[/tex] to know which equation it satisfies.
If we put [tex]y=3[/tex] then [tex]x=-2[/tex].
So working with option A.
[tex]y<-\frac{2}{5}x-2[/tex]
Plugging the values.
[tex]3<-\frac{2}{5}x-2\ ,3<\frac{-2x-10}{5}\ ,15<-2x-10\ ,15+10< -2x\ ,x=\frac{25}{-2}=-12.5[/tex]
And we know that [tex]x[/tex] must be equal to [tex]-2[/tex] so this is not the right answer.
We are left with only one choice that is C .
So option C is the correct option of the above inequality.
