Question

Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply. (–3, –2) (–2, 1) (–1, –2) (–1, 2) (1, –2) (1, 2)

Answer 1

1/2 is linear inequality

Answer 2

A)
`(-3,-2)`

C)
`(-1,-2)`

E)
`(1,-2)`

F)
`(1,2)`

Explanation:

we have

`y<0.5x+2`

we know that

If a ordered pair is a solution of the inequality

then

the ordered pair must be satisfy the inequality

Verify

Point A)
`(-3,-2)`

Substitute the value of x and value of y in the inequality an compare

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

`-2<0.5` -------> is true

The ordered pair
`(-3,-2)` is a solution of the inequality

Point B)
`(-2,1)`

Substitute the value of x and value of y in the inequality an compare

`1<0.5(-2)+2`

`1<1` -------> is not true

The ordered pair
`(-2,1)` is not a solution of the inequality

Point C)
`(-1,-2)`

Substitute the value of x and value of y in the inequality an compare

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

`-2<1.5` -------> is true

The ordered pair
`(-1,-2)` is a solution of the inequality

Point D)
`(-1,2)`

Substitute the value of x and value of y in the inequality an compare

`2<0.5(-1)+2`

`2<1.5` -------> is not true

The ordered pair
`(-1,2)` is not a solution of the inequality

Point E)
`(1,-2)`

Substitute the value of x and value of y in the inequality an compare

`-2<0.5(1)+2`

`-2<2.5` -------> is true

The ordered pair
`(1,-2)` is a solution of the inequality

Point F)
`(1,2)`

Substitute the value of x and value of y in the inequality an compare

`2<0.5(1)+2`

`2<2.5` -------> is true

The ordered pair
`(1,2)` is a solution of the inequality