Question

Which inequality will have a solid boundary line and a shaded region above its graph?

x − y ≥ 3



2x − 3y ≤ 3



3y − x < 2



2x + y < 7

Answer 1

A solid line means either ≥ or ≤

So either A or B

Above the graph: Must be greater than y

B

Answer 2

B. 2x − 3y ≤ 3

Explanation:

We are required to find the graph having solid boundary line.

When a graph have soled boundary line. Then, the inequality will have the equality sign in it.

That is, strict inequality can never have a solid boundary line.

So, option C and D are discarded.

Further, the graph must have shaded region above the graph.

Now, the region above the graph means that, the inequality must be of the form
`y > ax+b`.

So, we have,

`x-y\geq 3` implies
`y\leq x-3`

So, option A is not correct.

But,
`2x-3y\leq 3` implies
`y\geq (2x)/(3)-1`

Thus, the inequality having solid boundary and graph above is
`2x-3y\leq 3`.