GIven:
The equation of a line is 15x+12y=-108.
The objective is to find the slope of the perpencidular line.
It is known that the equation of straight line is,
[tex]y=mx+c[/tex]Here, m represents the slope of the equation and c represents the y intercept of the equation.
Let's find the slope of the given equation by rearranging the eqation.
[tex]\begin{gathered} 15x+12y=-108 \\ 12y=-108-15x \\ y=-\frac{15x}{12}-\frac{108}{12} \\ y=-\frac{5}{4}x-9 \end{gathered}[/tex]By comparing the obtained equation with equation of striaght line, the value of slope is,
[tex]m_1=-\frac{5}{4}[/tex]THe relationship between slopes of a perpendicular lines is,
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{5}{4}\cdot m_2=-1 \\ m_2=-1\cdot(-\frac{4}{5}) \\ m_2=\frac{4}{5}^{} \end{gathered}[/tex]Hence, the value of slope of perpendicular line to the given line is 4/5.
