Question

What is the equation of the line parallel to y=x-1 that contains the point (1,2)?

Answer 1

Parallel means the lines must have the same slope. The slope of y=x-1 is 1 because lines are expressed in the format y=mx+b where m=slope. This line has no m value and is therefore understood to be 1.
So all lines parallel to y=x-1 has the expression y=1x+b or simply y=x+b.
You are given the x and y values from the given point, so next you can substitute them into the expression.
y=x+b expression
2=1+b substitute x and y values from point
2-1=1-1+b Subtract 1 from both sides
1=b

Next, put the b value you have just found (y-intercept) and the m value (slope) together to define the equation of the line

y=x+1