llin999
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What is the slope of a line perpendicular to the line whose equation is 15x+18y=270. Fully simplify your answer.

Sagot :

VirαtKσhli

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 !

Step-by-step explanation:

hope it's helpful thanks

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