Question

Which point is in the solution set for y < x+2? Explain your answer.

Question 4 options:

(0, 2) because when you graph y < x+2, it is a point on the boundary line.


(1, 4) because when you graph y < x+2, it is a point that lies above the boundary line.


(-2, 0) because when you graph y < x+2, it is the x-intercept of the boundary line.


(2, 1) because when you graph y < x+2, it is a point that lies below the boundary line.

Answer 1

(2, 1) because when you graph y < x+2, it is a point that lies below the boundary line.

Explanation:

The given inequality is \[y<x+2\]

4 points are provided for evaluation if they belong to the solution set.

1) (0,2) : Substituting in the inequality - 2 < 0 + 2

Or, 2<2 which is false.

So, (0,2) does not belong to the solution set.

2) (1,4) : Substituting in the inequality - 4 < 1 + 2

Or, 4<3 which is false.

So, (1,4) does not belong to the solution set.

3) (-2,0) : Substituting in the inequality - 0 < -2 + 2

Or, 0<0 which is false.

So, (-2,0) does not belong to the solution set.

4) (2,1) : Substituting in the inequality - 1 < 2 + 2

Or, 1<4 which is true.

So, (2,1) does belong to the solution set.