Question

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

Answer 1

1st Graph is correct.

Explanation:

Given: Point ( -1 , -4 )

To find : Graph in which given point belong.

We find by putting given point in each graph.

Graph 1).

y ≤ -x + 4

LHS = y = -4

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

LHS ≤ RHS.

So, Given point belong to this graph.

Graph 2).

y ≤ -x - 6

LHS = y = -4

RHS = -x - 6 = -(-1) - 6 = 1 - 6 = -5

LHS ≥ RHS.

So, Given point does not belong to this graph.

Graph 3).

y ≤ 2x - 3

LHS = y = -4

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

LHS ≥ RHS.

So, Given point does not belong to this graph.

Graph 4).

y ≤ 5x - 1

LHS = y = -4

RHS = 5x - 1 = 5(-1) - 1 = -5 - 1 = -6

LHS ≥ RHS.

So, Given point does not belong to this graph.

Therefore, 1st Graph is correct.

Answer 2

The answer is y ≤ -x + 4 ⇒ the first answer

Explanation:

∵ The point is (-1 , -4)

∵ y ≤ -x + 4 ⇒ -1 ≤ -(-1) + 4

∴ -1 ≤ 5 ⇒ right inequality

If we try the others

y ≤ -x - 6 ⇒ -1 ≤ -(-1) - 6 ⇒ -1 ≤ -5 not true

y ≤ 2x - 3 ⇒ -1 ≤ 2(-1) - 3 ⇒ -1 ≤ -5 not true

y ≤ 5x - 1 ⇒ -1 ≤ 5(-1) - 1 ⇒ -1 ≤ -6 not true

∴ The answer is first one