Answer:
6/5
Step by step explanation:
Here we are provided with a equation which is ,
[tex]\longrightarrow 15x + 18y = 270 [/tex]
And we are interested in finding the slope of the line which is perpendicular to the given line. We may rewrite the equation as ,
[tex]\longrightarrow 18y = -15x +270\\ [/tex]
[tex]\longrightarrow y =\dfrac{-15x+270}{18}\\[/tex]
[tex]\longrightarrow y =\dfrac{-15}{18}x +\dfrac{270}{8}\\ [/tex]
[tex]\longrightarrow y =\dfrac{-5}{6}x +\dfrac{135}{4} [/tex]
Recall the slope intercept form of the line which is y = mx + c .On comparing to which we get ,
[tex]\longrightarrow m =\dfrac{-5}{6} [/tex]
Again , recall that product of slopes of two perpendicular lines is -1. So that ,
[tex]\longrightarrow m_{\perp} =-\bigg(\dfrac{1}{m}\bigg)[/tex]
Hence ,
[tex]\longrightarrow\underline{\underline{ m_{\perp}= \dfrac{6}{5}}}[/tex]
And we are done !
