Question 1089376
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You are correct. The problem as stated is impossible to answer. There must be a typo somewhere. 


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Refer to the figure below
<img src = "https://i.imgur.com/SYRNWJS.png">
(Image generated by <a href = "https://www.geogebra.org/home?ggbLang=en">GeoGebra</a> which is free graphing software)


The graph of 3x+4y = 12 is shown in red. It passes through (0,3) which is the y intercept and (4,0) which is the x intercept


The angle is composed of two segments (green and purple). The terminal side is the purple segment. 
Imagine that B and C are fixed and cannot be moved, but A is allowed to roam around as long as both x and y coordinates are negative together.
In this example, the angle is 225 degrees.


Based on the figure, we see that line AB has a positive slope while the slope of 3x+4y = 12 is negative. 
No matter where A is placed (according to the conditions above), we cannot make AB have a negative slope. 
So it's impossible for AB to be parallel to 3x+4y = 12 (as the slopes must be equal for parallel lines to occur).
Which means that it's impossible for the terminal side to be parallel to 3x+4y = 12.


Much of what I'm saying, if not all of it, is simply a paraphrase of what you already wrote. So you have the correct logic and reasoning. I'm simply offering a slightly different viewpoint with an example drawing. Let me know if this helps or not. Thank you.
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