Answer :
If we have two perpendicular lines of slopes m₁ and m₂, then we have the following equation:
[tex]m_1\cdot m_2=-1\ldots(1)[/tex]From the problem, we have the line with equation 9x - 8y = 10. The slope-intercept form of this line is:
[tex]\begin{gathered} 9x-8y=10 \\ 8y=9x-10 \\ \Rightarrow y=\frac{9}{8}x-\frac{5}{4} \end{gathered}[/tex]Then, the slope of this line is:
[tex]m_1=\frac{9}{8}[/tex]Using (1), we can find the slope of any perpendicular line to this line. Then:
[tex]\begin{gathered} \frac{9}{8}\cdot m_2=-1 \\ \Rightarrow m_2=-\frac{8}{9} \end{gathered}[/tex]Additionally, we know that this line passes through the point (0, 0), so the point-slope form of the perpendicular line is:
[tex]y-0=-\frac{8}{9}(x-0)[/tex]And the corresponding slope-intercept form is:
[tex]y=-\frac{8}{9}x[/tex]