Question

Are the graphs of the lines in the pair parallel? Explain.

y = 4x + 6
–15x + 3y = –45



Yes, since the slopes are the same and the y-intercepts are the same.


Yes, since the slopes are the same and the y-intercepts are different.


No, since the y-intercepts are different.


No, since the slopes are different.

Answer 1

To determine if the lines represented by the equations are parallel, we first need to find their slopes.

1. **For the first line:**
The equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Here, the slope \( m_1 = 4 \).

2. **For the second line:**
The given equation is \( -15x + 3y = -45 \). We need to rearrange it into slope-intercept form.
Add \( 15x \) to both sides:
\[
3y = 15x - 45
\]
Now, divide everything by \( 3 \):
\[
y = 5x - 15
\]
Here, the slope \( m_2 = 5 \).

Now we can compare the slopes:
- The slope of the first line \( m_1 = 4 \).
- The slope of the second line \( m_2 = 5 \).

Since the slopes \( 4 \) and \( 5 \) are different, the lines are not parallel.

The correct answer is:
**No, since the slopes are different.**