Question

Please help having trouble!

Answer 1

Option C is the correct choice that is
`y<-(5)/(2)x-2`

Explanation:

As this is a multiple choice question we will reduce the options and work on it with the given points
`(0,-2),(-2,-3)`

Note:We know that
`\leq ,\geq` where there is
`=` sign associated with it have a straight line graph there is no breaking in the line.

And when there is simply
`<,>` 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
`(x,y)\ (-2,3)` to know which equation it satisfies.

If we put
`y=3` then
`x=-2`.

So working with option A.

`y<-(2)/(5)x-2`

Plugging the values.

`3<-(2)/(5)x-2\ ,3<(-2x-10)/(5)\ ,15<-2x-10\ ,15+10< -2x\ ,x=(25)/(-2)=-12.5`

And we know that
`x` must be equal to
`-2` 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.