To find the slope of a line given the equation of the line, first write it in slope-intercept form.So that it is written as y=mx+b. Then you can easily see the slope since it is the coefficient of the x variable, or the number in front of x.
Always remember
Y= mx+b
‘m’ is the slope
And ‘b’ is the y-intercept
In this particular equation (y=x-3)
the number that is in front of ‘ x’ is the slope..
If there is no number given .. we always consider it as ‘1’.
Therefore ‘1’ is the slope of the line...
If you want further explanation may be by drawing the graph.. please let me know...