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

Answer:

(-3,-2), (-1,-2), (1,-2)

Step-by-step explanation:

Each point on the plane is of the form (x,y). let's see which points satisfy the inequality $0.5x+2>y$

a)

$0.5(-3)+2=-1.5+2=0.5>-2$, then (-3,-2) satisfies the inequality.

b)

$0.5(-2)+2=-1+2=1$, then (-2,1) doesn't satisfy the inequality

c)

$0.5(-1)+2=-0.5+2=1.5>-2$, then (-1,-2) satisfies the inequality.

d)

$0.5(-1)+2=1.5<2$, then (-1,2) doesn't satisfy the inequality.

e)

$0.5(1)+2=0.5+2=2.5>-2$, then (1,-2) satisfies the inequality.

Answer 2

Answer:

(–3, –2), (–1, –2) and (1, –2)

Step-by-step explanation:

The given inequality is

$y<0.5x+2$

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),

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

$-2<-1.5+2$

$-2<0.5$

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

Similarly,

For (-2,1),

$1<0.5(-2)+2$

$1<1$

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

For (-1,-2),

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

$-2<1.5$

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

For (-1,2),

$2<0.5(-1)+2$

$2<1.5$

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

For (1,-2),

$-2<0.5(1)+2$

$-2<2.5$

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