Answer :
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
```
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
```
