Answer:
y = |x - 4| - 9.
Step-by-step explanation:
To shift the graph of y = |x| down by 9 units and to the right by 4 units, we can follow these steps: 1. Recall that shifting a graph involves adding or subtracting values to the original equation. To shift the graph down by 9 units, we will subtract 9 from the original equation. To shift the graph to the right by 4 units, we will subtract 4 from the variable x. 2. Apply the shifts to the equation y = |x|. Subtracting 9 from the equation gives y = |x| - 9. Subtracting 4 from the variable x gives y = |x - 4| - 9. 3. Simplify the equation. The absolute value of (x - 4) represents the distance of x from 4 on the number line. So, the equation y = |x - 4| - 9 means that the y-coordinate is equal to the distance of (x - 4) from 0 on the number line, minus 9. 4. Therefore, the equation of the new graph, after shifting the original graph y = |x| down by 9 units and to the right by 4 units, is y = |x - 4| - 9.