Question

1. (se) if the line (at the right) is reflected across the x - axis, which of the following is the graph of the new line?

Explanation:

Step1: Recall reflection rule

When a point $(x,y)$ is reflected across the $x - axis$, the new point is $(x, - y)$. For a line, this means that the $y$-coordinates of all points on the line change their signs. If the original line has a positive slope (going up - left to down - right as shown in the original image), after reflection across the $x - axis$, the line will have a negative slope (going down - left to up - right).

Step2: Analyze options

Option A has a positive - sloped line, so it is incorrect. Option B has a positive - sloped line, so it is incorrect. Option C has a positive - sloped line, so it is incorrect. Option D has a negative - sloped line which is consistent with the reflection of the given positive - sloped line across the $x - axis$.

Answer:

D.