Question

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything below the line is shaded. Which points are solutions to the linear inequality y < 0.5x + 2? Select three options. (–3, –2) (–2, 1) (–1, –2) (–1, 2) (1, –2)

Answer 1

A, C, E

(–3, –2), (–1, –2) and (1, –2)

Step-by-step explanation:

The given inequality is

We need to check which points are solutions to the linear inequality y < 0.5x + 2.

Check the inequality be each given point.

For (-3,-2),

The statement is true. It means (-3,2) is a solution of given inequality.

Similarly,

For (-2,1),

The statement is false. It means (-2,1) is not a solution of given inequality.

For (-1,-2),

The statement is true. It means (-1,-2) is a solution of given inequality.

For (-1,2),

The statement is false. It means (-1,2) is not a solution of given inequality.

For (1,-2),

The statement is true. It means (1,-2) is a solution of given inequality.

Answer 2

(–3, –2)

(–1, –2)

(1, –2)

Explanation:

we know that

If a ordered pair is a solution of the linear inequality, then the ordered pair must satisfy the inequality. The ordered pair must lie on the shaded are of the solution set

we have

`y< 0.5x+2`

The solution of the inequality is the shaded area below the dashed line
`y=0.5x+2`

Verify each ordered pair

Substitute the value of x and the value of y in the inequality and then compare the results

case 1) (–3, –2)

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

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

so

The ordered pair satisfy the inequality

therefore

The ordered pair is a solution of the inequality (the ordered pair lie on the shaded area of the solution set)

case 2) (–2, 1)

`1< 0.5(-2)+2`

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

so

The ordered pair not satisfy the inequality

therefore

The ordered pair is not a solution of the inequality (the ordered pair not lie on the shaded area of the solution set)

case 3) (–1, –2)

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

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

so

The ordered pair satisfy the inequality

therefore

The ordered pair is a solution of the inequality (the ordered pair lie on the shaded area of the solution set)

case 4) (–1, 2)

`2< 0.5(-1)+2`

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

so

The ordered pair not satisfy the inequality

therefore

The ordered pair is not a solution of the inequality (the ordered pair not lie on the shaded area of the solution set)

case 5) (1, –2)

`-2< 0.5(1)+2`

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

so

The ordered pair satisfy the inequality

therefore

The ordered pair is a solution of the inequality (the ordered pair lie on the shaded area of the solution set)

see the attached figure to better understand the problem