without graphing how can you tell how the graphs of y=x and y=x-1 are related

Answer 1

We know we have y=x and y = x-1 and we know that the slope of both of the lines are m=1 since there is no coefficient in front of the x in both equations. The only difference we see between both of the equations is the -1 at the end of the second equation. What does this tell us? This tells us that the second function is translated 1 unit below the origin. So now, without even graphing, we know that both equations are related because they have the same slope, and the only difference is that the second equation, y = x-1, is translated one unit below.

Answer 2

y = mx + b, m = the slope and b = the y-intercept.

You have two lines with the same slope and different y-intercepts. What does that mean to you?