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

Question

y = 4x + 6
–15x + 3y = –45

No, since the y-intercepts are different.

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

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

No, since the slopes are different.

Answer 1

To determine if the lines are parallel, we need to look at their slopes.

1. For the first line, \( y = 4x + 6 \), the slope (m) is 4.

2. Now, let's rewrite the second equation to find its slope. The second equation is:

   \[ -15x + 3y = -45 \]

   We can rearrange this into slope-intercept form (y = mx + b). First, solve for \(y\):

   \[ 3y = 15x - 45 \]

   Now divide everything by 3:

   \[ y = 5x - 15 \]

   The slope of this line is 5.

Now, we compare the slopes:

• The slope of the first line is 4.
• The slope of the second line is 5.

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

Thus, the correct answer is:

No, since the slopes are different.