Question
The equation of the line that passes through the points \( (7,3) \) and \( (-2,3) \) is either \( x=3 \) or \( y=3 \). Which one is it? \[ \begin{array}{l}x=3 \\ y=3\end{array} \]
Ask by Burton Ayala. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = 3 \).
Solution
To determine the equation of the line that passes through the points \( (7,3) \) and \( (-2,3) \), we can analyze the coordinates of the points.
1. **Identify the coordinates of the points:**
- Point 1: \( (7, 3) \)
- Point 2: \( (-2, 3) \)
2. **Check the y-coordinates:**
- Both points have the same y-coordinate, which is \( 3 \).
3. **Conclusion about the line:**
- Since both points have the same y-coordinate, the line is horizontal. The equation of a horizontal line is given by \( y = k \), where \( k \) is the constant y-value.
4. **Final equation:**
- Therefore, the equation of the line that passes through the points \( (7,3) \) and \( (-2,3) \) is \( y = 3 \).
Thus, the correct answer is \( y = 3 \).
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Simplify this solution Bonus Knowledge
The points \( (7,3) \) and \( (-2,3) \) both have the same y-coordinate, which is 3. This means the line is horizontal, running parallel to the x-axis, and will maintain that y-value for any x-value. Thus, the equation of the line is \( y = 3 \). If you visualize this line on a graph, you'd see that regardless of how far left or right you go (the x-values), the height (y-value) remains constant at 3. So, any point along this line will have the form \( (x, 3) \), confirming that \( y = 3 \) is the right equation!
