To determine if the equations \( y + 9.5 = 3(x + 1.5) \) and \( y - 8 = 3(x + 1) \) represent the same line, we need to convert both equations to slope-intercept form \( y = mx + b \).
Starting with the first equation: \[ y + 9.5 = 3(x + 1.5) \] Distributing the \( 3 \): \[ y + 9.5 = 3x + 4.5 \] Subtracting \( 9.5 \) from both sides: \[ y = 3x + 4.5 - 9.5 \] \[ y = 3x - 5 \]
Now for the second equation: \[ y - 8 = 3(x + 1) \] Distributing the \( 3 \): \[ y - 8 = 3x + 3 \] Adding \( 8 \) to both sides: \[ y = 3x + 3 + 8 \] \[ y = 3x + 11 \]
Now we can compare the two forms:
- From the first equation, we have \( y = 3x - 5 \).
- From the second equation, we have \( y = 3x + 11 \).
Since the two equations result in different constant terms (-5 and +11), they represent different lines.
The correct conclusion is: No, because they both convert to different equations in slope-intercept form.