Question

Which linear inequality is represented by the graph?

Answer 1

for this one, all you have to do is test out those points and see if you get a valid answer!! it's easier than it looks.

y < 0.5x + 2

then, you can either find these points on your graph to check them (easier for most), but some people prefer the other method which is just taking your answer choices and plugging them in:
(-3, -2)
-2 < 0.5(-3) + 2
-2 < -1.5 + 2
-2 < 0.5
then, you just ask yourself "is that true?" is -2 less than 0.5? and the answer is yes, that's true, so this point is a solution.

the same process repeats with the rest of them, but:
(-3, 2) is a solution.
(-2, 1) is not a solution.
(-1, -2) is a solution.
(-1, 2) is not a solution.
(1, 2) is a solution.
(1, -2) is not a solution.
(1, 2) is a solution.

Answer 2

The correct options are 1, 3, 5 and 6.

Explanation:

The given inequality is

`y<0.5x+2`

A point is the solution of a linear inequality, if it satisfy the inequality.

The given point is (-3,-2). Check whether this is a solution or not.

`(-2)<0.5(-3)+2`

`-2<0.5`

This statement is true. Therefore (-3,-2) is a solution.

The given point is (-2,1). Check whether this is a solution or not.

`(1)<0.5(-2)+2`

`1<1`

This statement is false. Therefore (-2,1) is not a solution.

The given point is (-1,-2). Check whether this is a solution or not.

`(-2)<0.5(-1)+2`

`-2<1.5`

This statement is true. Therefore (-1,-2) is a solution.

The given point is (-1,2). Check whether this is a solution or not.

`(2)<0.5(-1)+2`

`2<1.5`

This statement is false. Therefore (-1,2) is not a solution.

The given point is (1,-2). Check whether this is a solution or not.

`(-2)<0.5(1)+2`

`-2<2.5`

This statement is true. Therefore (1,-2) is a solution.

The given point is (1,2). Check whether this is a solution or not.

`(2)<0.5(1)+2`

`2<2.5`

This statement is true. Therefore (1,2) is a solution.

Thus the correct options are 1, 3, 5 and 6.