Parallel to; through (-4,1)

 " y =  x + 4 " .
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Explanation:
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We are given an equation in "slope intercept form" ; that is; in the form of :

"y = mx + b" ;  in which "y" in isolated on the left-hand side of the equation; with "no-coefficient" (except for the "implied coefficient" of "1");  

                      in which: "m" is the slope of the line; and the coefficient of "x";  and "b" is the "y-intercept" (or the value of the "y-coordinate" of the graph when "x = 0" ;  
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  We are given:  " y = x − 4 " ;  
 
in which the slope; "m", is "" .

Since we want to write the equation, in slope-intercept form, for the line PARALLEL to the given line; we known that the "line" that is "parallel" will have the same slope".

So we can write:  " y = x + b" .  

Note that we are instructed to find the "parallel line" that passed through:

 "(-4, 1)" ; 
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So, in the aformentioned equation, we substitute "-4" for "x" ; and "1" for "y"; to solve for "b" ;
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   y = x + b ;

   1  =   * -4  + b ;

→  1 = -3 + b ;

↔ b + (-3) = 1 ;    

↔ b − 3 = 1 ;  

Add "3" to each side of the equation:

b − 3 + 3 = 1 + 3 ;

→ b = 4  .  
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Now, since we now that "b" is "positive 4" ; we can write the equation of the parallel line:

" y = x + 4 " .
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