Let's analyze the problem step by step to find which line equation could have a slope of 0.
1. Understanding the slope of a line:
- The slope of a line is a measure of its steepness.
- A slope of 0 means that the line is completely horizontal and does not rise or fall as it moves from left to right.
2. Form of the equation for a horizontal line:
- The equation of a horizontal line always has the form [tex]\( y = c \)[/tex], where [tex]\( c \)[/tex] is a constant.
- This indicates that [tex]\( y \)[/tex] remains the same for any value of [tex]\( x \)[/tex].
3. Evaluating the options:
- Option A: [tex]\( x = 0 \)[/tex]
- This equation represents a vertical line passing through [tex]\( x = 0 \)[/tex].
- A vertical line has an undefined slope, so this option is incorrect.
- Option B: [tex]\( y = 1 \)[/tex]
- This equation represents a horizontal line where [tex]\( y \)[/tex] is always 1, no matter the value of [tex]\( x \)[/tex].
- A horizontal line has a slope of 0, making this option correct.
- Option C: [tex]\( x = y \)[/tex]
- This equation represents a line where the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are always equal.
- This line has a slope of 1 (since for every unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] also increases by the same amount), so this option is incorrect.
- Option D: [tex]\( y = -x \)[/tex]
- This equation represents a line with a negative slope of -1.
- The slope is not zero, so this option is incorrect.
4. Conclusion:
- After evaluating all the options, the only equation that matches the criteria of a line with a slope of 0 is Option B: [tex]\( y = 1 \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{2} \)[/tex], confirming that the line with a slope of 0 is given by the equation [tex]\( y = 1 \)[/tex].
