Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Select the correct answer.

Which statement correctly describes the graph of [tex]\( y = x - 13 \)[/tex]?

A. It is the graph of [tex]\( y = x \)[/tex] translated 13 units up.
B. It is the graph of [tex]\( y = x \)[/tex] translated 13 units to the right.
C. It is the graph of [tex]\( y = x \)[/tex] translated 13 units to the left.
D. It is the graph of [tex]\( y = x \)[/tex] where the slope is decreased by 13.


Sagot :

To determine how the graph of [tex]\( y = x \)[/tex] is transformed by the equation [tex]\( y = x - 13 \)[/tex], let's carefully examine the transformations involved:

1. Understanding the Base Graph:
The base graph is [tex]\( y = x \)[/tex], which is a straight line passing through the origin (0,0) with a slope of 1. For each unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] also increases by one unit.

2. Identifying the Transformation:
The given equation is [tex]\( y = x - 13 \)[/tex]. In this equation, [tex]\( -13 \)[/tex] is a constant term being subtracted from [tex]\( x \)[/tex].

3. Interpreting the Transformation:
The addition or subtraction of a constant outside of the function (i.e., not multiplied by [tex]\( x \)[/tex]) represents a vertical shift of the graph:

- If it were [tex]\( y = x + 13 \)[/tex], the graph of [tex]\( y = x \)[/tex] would be translated upward by 13 units.
- Since it's [tex]\( y = x - 13 \)[/tex], the graph of [tex]\( y = x \)[/tex] is translated downward by 13 units.

Therefore, the correct statement that describes the graph of [tex]\( y = x - 13 \)[/tex] is:
- It is the graph of [tex]\( y = x \)[/tex] translated 13 units down.

Given the options, the correct answer is:
A. It is the graph of [tex]\( y = x \)[/tex] translated 13 units down.

Hence, the answer is:
```
A
```