Question 443624
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Write the slope-intercept equation for the line that passes through (-7, 6) and is perpendicular to -7x + 9y = -2 
Please show all of your work.
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        Strictly saying, the solution and the answer in the post by @mananth are incorrect.


        Indeed, if I substitute coordinates  (-7,6)  into his equation  y = -1.29x-3, 

        I will get  y = -1.29*(-7) + 6 = 6.03,  but not precisely  6,

        which means that the point  (-7,6)  does not lie on the line.


        In this my post,  I will present a correct precise solution and the correct answer,  and then will explain, 

        WHY  the solution by @mananth is wrong.



<pre>
Any line perpendicular to the given line -7x + 9y = -2  has an equation of the form

    7y + 9x = c   (1)


where 'c' is some real constant.  So, we only need to find the value of 'c'.


To do it, we substitute the coordinates of the given point (-7,6) into equation (1)

    7*6 + 9*(-7) = 42 - 63 = -21.


So, the sough equation is

    7y + 9x = -21.


It is NOT that equation, which is presented as the answer in the post by @mananth.
</pre>

So, &nbsp;I solved the problem correctly, and my answer is different from that by @mananth.


The error made by @mananth, &nbsp;is that he replaced the precise value &nbsp;m1 = {{{7/9}}} &nbsp;of the slope
of the original line by the decimal value &nbsp;0.78.


This value, &nbsp;0.78, &nbsp;is only approximation, &nbsp;but not the precise rational value.


So, &nbsp;the error by @mananth is that he uses his computer code in the form, &nbsp;which &nbsp;IS &nbsp;NOT &nbsp;APPLICABLE
and &nbsp;IS &nbsp;NOT &nbsp;ADEQUATE &nbsp;to the problem.