To which graph does the point (–1, –4) belong?
y < –x + 4
y < –x – 5
y < 2x – 3
y < 5x + 1
6 Answers

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