Hello, the answer should be [tex]m=\frac{6}{5}= 1,2[/tex].
First, let's edit the given function as [tex]y[/tex] parameter leave alone.
[tex]15x+18y=270\\\\18y=270-15x\\\\y=\frac{270-15x}{18}\\ \\y=\frac{270}{18}-\frac{15x}{18}[/tex]
IMPORTANT!
If the given equation looks like;
[tex]y=f(x)\\\\y=ax+b[/tex]
then, the slope of the equation is the coefficient of [tex]x[/tex] parameter ([tex]a[/tex])
The slope(m);
[tex]m=\frac{-15}{18}=\frac{-5}{6}[/tex]
The product of the slopes of two perpendicular lines must be [tex]-1[/tex]. By that way, the slope of a line perpendicular to the given line is below:
[tex]m_{expected}=\frac{-1}{m_{given}} \\\\m_{expected}=\frac{-1}{\frac{-5}{6} }=\frac{6}{5}[/tex]
Good luck. If you have any questions, then feel free to ask in comments!
