Answer
The slope of a line that is parallel to the graph of the equation is $1$.
Work Step by Step
We are given $y=x+3$.
Nonvertical lines are parallel if they have the same slope and different y-intercepts.
Write an equation in slope-intercept form of the line, where m represents the slope:
$y=mx+b$
$y=1x+3$
Therefore, the slope of a line that is parallel to the graph of the equation is $1$.