Question 1204341
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Answer:  <font color=red>7x - 9y = -72</font> (option C)



Reason


Multiply both sides by 9 to clear out the denominator.
Then we'll rearrange things so the variable terms are on the left hand side (LHS) while the constant is on the right hand side (RHS)


Here is one way to write out the steps
y = (7/9)x + 8
9y = 9*( (7/9)x + 8 )
9y = 9*(7/9)x + 9*8 .... don't forget to distribute all the way through
9y = 7x + 72
9y-7x = 72
-7x+9y = 72


At this point we should be done. In some math textbooks that would be the case. 
However, other math textbooks require the standard form Ax+By = C to have A > 0.
It appears that your textbook has this requirement.


To make the x coefficient be positive, multiply both sides by -1
-7x+9y = 72
-1*(-7x+9y) = -1*72
<font color=red>7x - 9y = -72</font>
And we're done.


To check the answer, use Desmos or GeoGebra to graph 7x-9y = -72 and y = (7/9)x+8 to see that they produce the exact same line.
<a href = "https://www.desmos.com/calculator/edykrshgaz">https://www.desmos.com/calculator/edykrshgaz</a>


Another way to check the answer would be to type <font color=blue>Solve 7x-9y = -72 for y</font> into WolframAlpha. The result it displays is {{{y = (7x)/9 + 8}}} which is the same as {{{y = expr(7/9)x+8}}} or y = (7/9)x + 8.
<a href = "https://www.wolframalpha.com/input?i=Solve+7x-9y+%3D+-72+for+y">https://www.wolframalpha.com/input?i=Solve+7x-9y+%3D+-72+for+y</a>
There are many other CAS (computer algebra system) calculators that can do the same thing. 


GeoGebra has a CAS feature. For GeoGebra, the input would be <font color=blue>Solve[7x-9y=-72,y]</font>. 
Do not type that into the normal input bar. Instead you need to switch to CAS mode.
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