To determine if the equations \( y - 1.5 = 5(x + 6.5) \) and \( y + 8.5 = 5(x + 8.5) \) represent the same line, we need to convert both equations into slope-intercept form ( \( y = mx + b \) ).
Converting the first equation:
- Start with \( y - 1.5 = 5(x + 6.5) \).
- Distribute the 5: \[ y - 1.5 = 5x + 32.5 \]
- Add 1.5 to both sides: \[ y = 5x + 34 \]
Converting the second equation:
- Start with \( y + 8.5 = 5(x + 8.5) \).
- Distribute the 5: \[ y + 8.5 = 5x + 42.5 \]
- Subtract 8.5 from both sides: \[ y = 5x + 34 \]
Both equations simplify to \( y = 5x + 34 \).
Therefore, they represent the same line.
The correct conclusion is:
Yes, because they both convert to \( y = 5x + 34 \) in slope-intercept form.