Question 423677
what is the equation of a line that passes through (-5, 1) and is parallel to y = x + 4 ?

Parallel lines have the same slope.  Therefore, we know the equation has the form y = x + b.  The only thing left to do is find the y-intercept.  The slope of a line can be determined using two points on the line: m = (y2-y1)/(x2-x1).
Let's use the y-intercept as one of the points.  Since x=0 at the y-intercept, we have:
m = 1 = (b-1)/(0 - -5).  Solving for b gives (b - 1) = 5 -> b = 6.  
So our equation is y = x + 6
{{{graph(300,200,-10,10,-10,10,x+4,x+6)}}}