Use the image to answer the question.

Question

A coordinate plane shows four quadrants with both the axes ranging from negative 5 to 5 in unit increments. Two points are plotted, with a dashed line passing through them. The dashed line passes through two points marked at left parenthesis 2 comma 0 right parenthesis and left parenthesis 0 comma negative 2 right parenthesis. The line extends beyond both points. The area below the dashed line is shaded.

Given the solution set of an inequality in two variables, identify the inequality symbol that matches the inequality on the graph.

(1 point)
x − y 3

Answer 1

To identify the correct inequality symbol based on the graph and the dashed line given, we first need to analyze the points through which the dashed line passes. The points are (2, 0) and (0, -2).

We can find the equation of the line passing through these points using the slope formula:

1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 0}{0 - 2} = \frac{-2}{-2} = 1 \]

2. Use the slope-intercept form \(y = mx + b\) to find the y-intercept (b). Using point (2, 0): \[ 0 = 1(2) + b \implies b = -2 \] Thus, the equation of the line is: \[ y = x - 2 \]

Now, we rearrange this equation to find the inequality associated with the shaded area below the dashed line:

\[ y < x - 2 \]

Given that the line is dashed, it indicates that points on the line are not included in the solution set. Therefore, we use the "<" symbol.

Finally, the inequality represented on the graph is: \[ y < x - 2 \]

This implies the answer to your question is:

\[ x - y > 2 \] (when rearranging the terms, as it is equivalent to \(y < x - 2\)).