Use the image to answer the question.

Question

A dotted line drawn on a coordinate plane slopes downward from top left to bottom right. The part of the plane above and to the right of the line is shaded. Both axes range from negative 10 to 10 in unit increments.

Write an equation for the linear inequality in the provided graph. Which option is the correct equation for the graph?

Option #1: y≥−x−2


Option #2: y>−x−2


Option #3: y≤−x−2


Option #4: y<−x−2


(1 point)
The equation that matches the graph is Option #
.

Answer 1

To find the correct equation for the linear inequality that corresponds to the described graph, we first analyze the characteristics of the line and the shading.

The dotted line that slopes downward from the top left to the bottom right indicates that the inequality will not include the line itself, which suggests we will use a "greater than" or "less than" symbol (not "greater than or equal to" or "less than or equal to").

Next, since the area above and to the right of the line is shaded, this means we want the values of \( y \) to be greater than the values on the line. The equation of the line appears to be \( y = -x - 2 \).

Given this information, the correct inequality that represents the graph is:

Option #2: y > −x − 2

Thus, the equation that matches the graph is Option 2.