Question

Slopes of parallel \perpendicular lines

Answer 1

Hello, the answer should be $m=\frac{6}{5}= 1,2$.

First, let's edit the given function as $y$ parameter leave alone.

$15x+18y=270\\\\18y=270-15x\\\\y=\frac{270-15x}{18}\\ \\y=\frac{270}{18}-\frac{15x}{18}$

IMPORTANT!

If the given equation looks like;

$y=f(x)\\\\y=ax+b$

then, the slope of the equation is the coefficient of $x$ parameter ($a$)

The slope(m);

$m=\frac{-15}{18}=\frac{-5}{6}$

The product of the slopes of two perpendicular lines must be $-1$. By that way, the slope of a line perpendicular to the given line is below:

$m_{expected}=\frac{-1}{m_{given}} \\\\m_{expected}=\frac{-1}{\frac{-5}{6} }=\frac{6}{5}$

Good luck. If you have any questions, then feel free to ask in comments!