Let's solve the problem step by step.
First, we need to understand what happens when a line segment is dilated from the origin. Dilating a line segment means that we scale both the coordinates of its endpoints by a given scale factor.
Given that the line segment [tex]\(\overline{XY}\)[/tex] has a slope [tex]\(m\)[/tex], we need to determine the slope of [tex]\(\overline{X^{\prime}Y^{\prime}}\)[/tex] after the dilation.
A dilation with the origin as the center does not change the angle between the line and the coordinate axes. Therefore, the direction of the line remains the same, which means the slope of the line remains unchanged.
So, if we dilate [tex]\(\overline{XY}\)[/tex] with a scale factor of 1.3, the slope of the resulting line [tex]\(\overline{X^{\prime}Y^{\prime}}\)[/tex] will still be [tex]\(m\)[/tex].
Therefore, the slope of [tex]\(\overline{X^{\prime}Y^{\prime}}\)[/tex] is:
[tex]\[ \boxed{m} \][/tex]
The correct answer is:
[tex]\[ \mathbf{D.} \, m \][/tex]
