Which of the following inequalities is represented by the shaded region of the graph below ?

A.) y ≤ x + 1 or y ≥ x - 3

B.) y ≥ x + 1 or y ≤ x - 3

C.) y ≤ x + 1 or y ≥ (-3/2)x + 3

D,) y ≤ x + 1 or y ≤ (-3/2)x - 3

E.) y ≤ x + 1 or y ≥ (-3/2)x - 3

B.) y ≥ x + 1 or y ≤ x - 3

C.) y ≤ x + 1 or y ≥ (-3/2)x + 3

D,) y ≤ x + 1 or y ≤ (-3/2)x - 3

E.) y ≤ x + 1 or y ≥ (-3/2)x - 3

**When graphing inequalities:**

**≤ and ≥ signs indicate a solid boundary line, while < and > signs indicate a dashed boundary line****shading below the line indicates use of < or ≤ signs****shading above the line indicates > or ≥ signs**

First, locate the y-intercept of each line, while also determining the slope of each line.

**One line**y-intercept is 1

slope is 1

Equation is y = x + 1

Also, the shading is below that line, and it is a solid line,

Therefore, the inequality is:

**y ≤ x + 1**{boundary line is y = x + 1, using ≤ sign because of solid line, using ≤ sign because of shading below}

**Other line**y-intercept is -3

slope is -3/2

Equation of boundary line is y = (-3/2)x - 3

Also, the shading is above that line, and it is a solid line.

Therefore, the inequality is:

**y ≥ (-3/2)x - 3**{boundary line is y = (-3/2)x - 3, using ≥ sign because of solid line, using ≥ sign because of shading above}

Put the two together, and you have:

**E.) y ≤ x + 1 or y ≥ (-3/2)x - 3**

**Ask Algebra House**