Question

The graph of y > 1 2 x - 2 is shown. Which set contains only points that satisfy the inequality? A) {(6, 1), (-1, -3), (4, 4)} B) {(1, -1), (-3, -3), (2, 4)} C) {(1, -1), (-3, -3), (4, -2)} D) {(-1, -3), (-3, -3), (2, 4)}

Answer 1

Answer:

Option B) {(1, -1), (-3, -3), (2, 4)}

Step-by-step explanation:

The correct inequality is

$y>\frac{1}{2}x-2$

The solution of the inequality is the shaded area above the dashed line $y=\frac{1}{2}x-2$

see the attached figure to better understand the problem

we know that

If a ordered pair satisfy the inequality, then the ordered pair must lie in the shaded area of the solution

Verify each case

case A) {(6, 1), (-1, -3), (4, 4)}

ordered pair (6,1)

For x=6, y=1

substitute in the inequality

$1>\frac{1}{2}(6)-2$

$1>1$ ---> is not true

therefore

The point not satisfy the inequality

case B)  {(1, -1), (-3, -3), (2, 4)}

ordered pair (1,-1)

For x=1, y=-1

substitute in the inequality

$-1>\frac{1}{2}(1)-2$

$-1>-1.5$ ---> is true

so

The point satisfy the inequality

ordered pair (-3,3)

For x=-3, y=3

substitute in the inequality

$3>\frac{1}{2}(-3)-2$

$3>-3.5$ ---> is true

so

The point satisfy the inequality

ordered pair (2,4)

For x=2, y=4

substitute in the inequality

$4>\frac{1}{2}(2)-2$

$4>-1$ ---> is true

so

The point satisfy the inequality

therefore

The set contains only points that satisfy the inequality

case C) {(1, -1), (-3, -3), (4, -2)}

ordered pair (4,-2)

For x=4, y=-2

substitute in the inequality

$-2>\frac{1}{2}(4)-2$

$-2>0$ ---> is not true

therefore

The point not satisfy the inequality

case D) {(-1, -3), (-3, -3), (2, 4)}

ordered pair (-1,-3)

For x=-1, y=-3

substitute in the inequality

$-3>\frac{1}{2}(-1)-2$

$-3>-2.5$ ---> is not true

therefore

The point not satisfy the inequality