Question

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.

Which point is a solution to the linear inequality y < Negative one-halfx + 2?

(2, 3)
(2, 1)
(3, –2)
(–1, 3)

Answer 1

To determine which point is a solution to the linear inequality y<−12x+2y<−21​x+2, we can check each point's coordinates one by one.

Let's test each point:

Explanation:

Point (2, 3):

Substitute x = 2 and y = 3 into the inequality:

3<−12(2)+23<−21​(2)+2

3<−1+23<−1+2

3<13<1

Since 3<13<1 is not true, this point is not a solution to the inequality.

Point (2, 1):

Substitute x = 2 and y = 1 into the inequality:

1<−12(2)+21<−21​(2)+2

1<−1+21<−1+2

1<11<1

Again, 1<11<1 is not true, so this point is also not a solution to the inequality.

Point (3, -2):

Substitute x = 3 and y = -2 into the inequality:

−2<−12(3)+2−2<−21​(3)+2

−2<−32+2−2<−23​+2

−2<−12−2<−21​

This time, −2<−12−2<−21​ is true, so this point is a solution to the inequality.

Point (-1, 3):

Substitute x = -1 and y = 3 into the inequality:

3<−12(−1)+23<−21​(−1)+2

3<12+23<21​+2

3<523<25​

3<523<25​ is true, so this point is also a solution to the inequality.

Therefore, the points that are solutions to the inequality are:

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