Answer:
[tex](-5/8)[/tex].
Explanation:
In a cartesian plane, two lines are perpendicular to each other if and only if the product of their slopes is [tex](-1)[/tex]. If line [tex]{\rm S}[/tex] of slope [tex]m_{\rm S}[/tex] and line [tex]{\rm T}[/tex] of slope [tex]m_{\rm T}[/tex] are perpendicular to each other, their slopes should satisfy:
[tex]m_{\rm S} \, m_{\rm T} = (-1)[/tex].
In this question, it is given that the slope of line [tex]{\rm S}[/tex] is [tex]m_{\rm S} = (8/5)[/tex]. Rearrange the equation [tex]m_{\rm S} \, m_{\rm T} = (-1)[/tex] to find the slope of line [tex]{\rm T}[/tex]:
[tex]\begin{aligned}m_{\rm T} &= \frac{(-1)}{m_{\rm S}} = \frac{-1}{8/5} = -\frac{5}{8}\end{aligned}[/tex].
In other words, the slope of line [tex]{\rm T}[/tex] should be [tex](-5/8)[/tex].
The slope of line T, which is perpendicular to line S, is -5/8.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
Therefore, if line S has a slope of 8/5, the slope of line T would be -5/8.
In general, if the slope of a line is m, the slope of a line perpendicular to it would be -1/m.
