Question 423677
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what is {{{highlight(cross(the))}}} <U>an</U> equation of a line that passes through (-5, 1) and is parallel to y = x + 4 ?
please show steps to help me understand
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution in the post by @matanth is &nbsp;FATALLY &nbsp;WRONG &nbsp;and conceptually &nbsp;INCORRECT.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It contains arithmetic errors and does not satisfy the imposed conditions.
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;His line is not parallel to the given line. 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came to provide a correct solution.



<pre>
Any line parallel to y = x + 4  has a form  y = x + c  with some constant 'c'.

The only thing is to determine the value of 'c'.


We use the given point (-5,1}: value of 'c' is determined by this equation y = x + c
after substituting coordinates of the point

    1 = -5 + c,

    c = 1 - (-5) = 1 + 5 = 6.


<U>Answer</U>.  Equation of the line parallel to  y = x+4  and passing through (-5,1)  is y = x + 6. 
</pre>

Solved.