Problem Solving

Source: veritas

Which of the following points falls outside of the region defined by 2y≤6x−12?

A. (5, 1)
B. (3, -8)
C. (2, 0)
D. (1, -2)
E. (0, -14)

can someone explain by using graph


OA D

Mechmeera wrote:Source: veritas

Which of the following points falls outside of the region defined by 2y≤6x−12?

A. (5, 1)
B. (3, -8)
C. (2, 0)
D. (1, -2)
E. (0, -14)

2y ≤ 6x - 12
y ≤ 3x - 6.

Every point (x, y) such that y ≤ 3x - 6 will be in the defined region.
Implication:
Any point (x, y) such that y > 3x - 6 will be OUTSIDE the defined region.

We can PLUG IN THE ANSWERS.
Note:
When the question stem includes the phrase which of the following, the correct answer is likely to be D or E.
Thus, we should WORK UP FROM E.
When the correct answer choice is plugged in, y > 3x - 6.

E: (0, -14)
Substituting x=0 and y=-14 into y > 3x - 6, we get:
-14 > 3*0 - 6
-14 > -6.
Doesn't work.
Eliminate E.

D: (1, -2)
Substituting x=1 and y=-2 into y > 3x - 6, we get:
-2 > 3*1 - 6
-2 > -3.
Success!

The correct answer is D.