If the graph of y = |x| is translated so that the point (1, 1) is moved to (4, 1), what is the equation of the new graph?

y = |x - 3|

You need an equation so that you need to add 3 to get the same value. Changing from 'x' to 'x - 3' requires a value (of the second expression) that is 3 larger than the entry in the first expression.