Question 454369
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Write an equation of the line containing the given point and parallel to the given line. 
Express your answer in the form y=mx+b
(-6,7); 2x=9y+8
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        The solution and the answer in the post by @mananth both are incorrect.

        They are incorrect, since @mananth permanently rounds rational fractions to decimal fractions

        even when it is not allowed and ruins the precise form of equations.


        So,  I came to make the job in a right way as it  SHOULD  be done.



<pre>
Any line parallel to  2x = 9y + 8  has the form

    2x = 9y + c,    (1)

where 'c' is a real constant.  To find 'c', we simply insert coordinates (-6,7) into equation (1)

    2*(-6) = 9*7 + c,

    -12 - 63 = c,

    c = -75.


Thus equation (1) takes the form

    2x = 9y - 75.    (2)


To get the form  y = mx + b, we express 'y' from equation (2)

    y = {{{(2/9)x}}} + {{{75/9}}},

or,  which is the same

    y = {{{(2/9)x}}} + 8{{{1/3}}}.    (3)


So, the slope of the sough line is  m = {{{2/9}}}  and its equation is  y = {{{(2/9)x}}} + 8{{{1/3}}}.
</pre>

Solved correctly.