# To which graph does the point (−1, 4) belong?

To which graph does the point (–1, –4) belong?

y < –x + 4

y < –x – 5

y < 2x – 3

y < 5x + 1

• Well, let's plug in the values we know for x and y to find out.

-4 <? -(-1) + 4

-4 <? 1 + 4

-4 <? 5

Yes. So the point is in this graph.

-4 <? -(-1) - 5

-4 <? 1 - 5

-4 <? -4

No. -4 is not less than itself. The point is outside this graph.

-4 <? 2(-1) - 3

-4 <? -2 - 3

-4 <? -5

No. -4 is not less than -5. The point is outside this graph.

-4 <? 5(-1) + 1

-4 <? -5 + 1

-4 <? -4

No. -4 is not less than itself. The point is outside this graph.

• (–1, –4) belongs to the graph of y < –x + 4 because (-4) < –(–1) + 4

• Y < -X + 4.

You put (-1) in for X & (-4) in for Y.

(-4) < -(-1) +4. -4 < 1 + 4. -4 < 5 is true.

(-4) < -(-1) - 5. -4 < 1 - 5. -4 < -4 is false.

-(4) < 2(-1) - 3. -4 < -2 -3. -4 < -5 is false.

(-4) < 5(-1) + 1. -4 < -5 + 1. -4 < -4 is false.

Source(s): Mah Braynz. (And a Graphing Calculator helps, too.)
• 1. put x = -4, and y= -1 in each inequality.

1st case y < -x + 4

=> -4 < -(-1) + 4

=> -4 < 1+5

=> -4 < 6 this is true.

but it is not true for rest of the cases,

Hence answer is y < -x + 4 .

• -4 <-(-1)+4

-4 < 1+4

-4 < 5

it belongs to this one since it comes out being correct

• Substituting the values for x and y

1] y < -x + 4

-4 < 1 + 4........................this is true