Final answer:
The translation from the graph y = (x - 5) + 7 to the graph of y = (x + 1) - 2 is a rightward shift by 6 units and downward shift by 9 units.
Step-by-step explanation:
The phrase that best describes the translation from the graph of y = (x - 5) + 7 to the graph of y = (x + 1) - 2 is a shift to the right by 6 units and down by 9 units. To see this, you need to understand how changes in the parameters of a linear equation affect its graph. The equation y = (x - 5) + 7 can be simplified to y = x + 2, which is a straight line with a slope of 1 and a y-intercept of 2. When you change the equation to y = (x + 1) - 2, which simplifies to y = x - 1, the slope remains the same since there is no change in front of the x term, but the y-intercept has changed from 2 to -1. This means the entire line shifts to the right 6 units and down 9 units.