Question

Write the inequality shown by the shaded region in the graph with the boundary line y = -2x - 5

Answer 1

Explanation:

The graph shows the inequality y≥−2x−5.

The line y=−2x−5 is the boundary line. On one side of the line are the points with y>−2x−5, and on the other side of the line are the points with y<−2x−5.

Let's test the point (0,0), which is inside of the shaded region, and determine which inequality describes the side of the boundary line that contains the test point.

At (0,0), which inequality is true?

The shaded region contains the point (0,0); therefore, the inequality that contains (0,0), y>−2x−5 has the correct shaded side.

Notice that since the boundary line is graphed with a solid line, the inequality includes the equal sign.

Answer 2

We do not have the image, so we can answer in a general way.

We know that the boundary line is y = -2*x - 5

We can have 4 cases:

1) a dashed line and the shaded part is above the line.

y > -2*x - 5

2) a dashed line and the shaded part is below the line

y < -2*x - 5

Here we have dashed lines because the values of the line are not solutions for the inequality.

3) a solid line and the shaded part is above the line.

y ≥ -2*x - 5

4) a solid line and the shaded part is below the line.

y ≤ -2*x - 5

Here we have solid lines because the values in the line itself are solutions.