Question

To which graph does the point (−1, 4) belong? y ≤ −x + 4 y ≤ −x − 5 y ≤ 2x − 3 y ≤ 5x + 1

Answer 1

By replacing the point (-1, 4) into the first inequality y<= -(x)+4
4<= - (-1)+4
4<=1+4
4<=5 (this implies that this is the answer).

Answer 2

Option A is correct.

Explanation:

Given coordinates of the point ( -1 , 4 )

Option A

y ≤ -x + 4

LHS = y = 4

RHS = -x + 4 = -(-1) + 4 = 5

LHS ≤ RHS

So, Given point belong to this graph.

Option B

y ≤ -x - 5

LHS = y = 4

RHS = -x - 5 = -(-1) - 5 = -4

LHS ≥ RHS

So, Given point does not belong to this graph.

Option C

y ≤ 2x - 3

LHS = y = 4

RHS = 2x - 3 = 2(-1) - 3 = -5

LHS ≥ RHS

So, Given point does not belong to this graph.

Option D

y ≤ 5x + 1

LHS = y = 4

RHS = 5x + 1 = 5(-1) + 1 = -4

LHS ≥ RHS

So, Given point does not belong to this graph.

Therefore, Option A is correct.