Question

To which graph does the point (8, −2) belong?

A. y ≤ −x + 4
B. y ≤ x − 11
C. y ≤ −2x − 3
D. y ≤ 2x + 1

Answer 1

If we substitute the values in we get....

A. -2 ≤ -4

B. -2 ≤ -3

C. -2 ≤ -19

D. -2 ≤ 17

As you can see the only true answer is D, so that would be your correct choice. :)

Answer 2

`\boxed{\boxed{y\leq 2x+1}}`

Explanation:

If a point lies on the shaded region, then it must satisfy the inequality.

So putting the coordinates of (8, -2) in all the inequalities.

A.
`y\leq -x+4`

`\Rightarrow -2\leq -8+4`

`\Rightarrow -2\\leqslant -4`

Therefore, it does not belong to this inequality.

B.
`y\leq x-11`

`\Rightarrow -2\leq 8-11`

`\Rightarrow -2\\leqslant -3`

Therefore, it does not belong to this inequality.

C.
`y\leq -2x-3`

`\Rightarrow -2\leq -16-3`

`\Rightarrow -2\\leqslant -19`

Therefore, it does not belong to this inequality.

D.
`y\leq 2x+1`

`\Rightarrow -2\leq 16+1`

`\Rightarrow -2\leq 17`

Therefore, it belongs to this inequality.