Question

Do the equations y+9.5=3(x+1.5) and y−8=3(x+1) represent the same line?

Yes, because they both convert to y=3x9.25 in slope-intercept form.

No, because they both convert to different equations in slope-intercept form.

Yes, because they both convert to y=3x−5 in slope-intercept form.

Yes, because they both convert to y=3x+11 in slope-intercept form.

Answer 1

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:
1. From the first equation, we have \( y = 3x - 5 \).
2. 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.**