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

Y=|x|+3

This can be found by graphing. The slope of this equation is assumed to be 1/1 and the y intercept is assumed to be 0. If this is translated upwards, we can see that when the line has a y-intercept of 3, it crosses the point (1,4).