Question

To which graph does the point (2, 4) belong?

y ≥ x + 3
y ≥ −x + 8
y ≥ 4x − 5
y ≥ −2x + 9

Answer 1

(2,4) belongs to the graph y is greater than or equal to 4x - 5

Answer 2

Option (3) is correct.

(2,4) belongs to y ≥ 4x - 5

Explanation:

Given : the point (2,4)

We have to find the equation of graph to which the point (2,4) belongs.

We will substitute the point in the each given equation and for which the point satisfies will contain the point.

For 1) y ≥ x + 3

Put x = 2 and y = 4

⇒ 4 ≥ 2 + 3

⇒ 4 ≥ 5 (false)

For 2) y ≥ -x + 8

Put x = 2 and y = 4

⇒ 4 ≥ -2 + 8

⇒ 4 ≥ 6 (false)

For 3) y ≥ 4x - 5

Put x = 2 and y = 4

⇒ 4 ≥ 4(2) - 5 = 8 - 5

⇒ 4 ≥ 3 (true)

For 4) y ≥ -2x + 9

Put x = 2 and y = 4

⇒ 4 ≥ -4 + 9

⇒ 4 ≥ 5 (false)

Since, the point (2,4) satisfies only inequality y ≥ 4x - 5.

Thus, (2,4) belongs to y ≥ 4x - 5