Question 120693
First, let's take a look at a few examples:

Consider,

A. {{{f(x)=3x-2}}}
B. {{{f(x)=3x+1}}}

Graph of A:
{{{graph(100,100,-5,5,-5,5,3x-2)}}}
Graph of B:
{{{graph(100,100,-5,5,-5,5,3x+1)}}}

Now, notice how these two lines are parallel when combined into the same graph:
{{{graph(100,100,-5,5,-5,5,3x-2,3x+1)}}}

Notice how y changes per increase in x for each graph. Further, notice that the constants in each equation just shift the line up or down. It shouldn't be surprising, then, that parallel lines have exactly the same slope.
Equation: {{{y=mx+b}}} is the slope-intercept form of a line. m is the slope, b is the intercept.
i.e.: take x=0, {{{y=b}}} implies (0,b) is where the line crosses the y-axis.


So, for the given problem, {{{y=x+6}}}, we have {{{m=1}}} and {{{b=6}}}. If we want to find the equation of a parallel line, m must be the same for the next line!

Now, consider the point-slope form of a line:
{{{y-y[1]=m(x-x[1])}}}. The given point in the problem will be our (x1,y1) That is, (4,5).

Then, 
{{{y-5=1(x-4)}}}
{{{y=x+1}}} is our line.