Select the correct answer.

Question

Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x − 13?
A.
It is the graph of y = x translated 13 units up.
B.
It is the graph of y = x translated 13 units to the right.
C.
It is the graph of y = x translated 13 units to the left.
D.
It is the graph of y = x where the slope is decreased by 13.

Answer 1

To determine the correct transformation of the graph of \( y = x \) for \( y = x - 13 \), we need to analyze the effect of the subtraction of 13.

The equation \( y = x - 13 \) can be interpreted as taking the original line \( y = x \) and shifting all \( y \)-values downward by 13 units. This is because for any given \( x \)-value, the \( y \)-value will be 13 units smaller than it would be in the original graph \( y = x \).

So, the correct description is:
- It is the graph of \( y = x \) translated 13 units down.

However, since no such option exists, and understanding that a downward shift by 13 is effectively a vertical shift, we should look at the intended correct transformation which should involve a simple translation but with an appropriate description.

None of the provided options exactly describe this. So based on interpreting the given options:

A. It is the graph of \( y = x \) translated 13 units up.
- Incorrect because it translates the graph in the opposite direction.

B. It is the graph of \( y = x \) translated 13 units to the right.
- Incorrect because this would affect the x-values instead.

C. It is the graph of \( y = x \) translated 13 units to the left.
- Incorrect because this would also affect the x-values.

D. It is the graph of \( y = x \) where the slope is decreased by 13.
- Incorrect because the slope remains unchanged at 1.

Given that none of the options appropriately match the transformation (vertical shift downward by 13) from the analysis above, it appears that there may be a mistake in the provided options.

Normally, the appropriate transformation would be best described as a vertical shift downward. However, in the context of these provided options:

None of the provided choices are correct if the intention was to describe a \( y \)-intercept shift.

The problem as stated doesn't correctly align with typical shift descriptions.