Question

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

y = 4x – 4
24x – 4y = 96


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


No, since the slopes are different.


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


No, since the y-intercepts are different.

Answer 1

To determine if the graphs of the lines are parallel, we need to compare their slopes.

1. For the first equation, \( y = 4x - 4 \), the slope (m) is 4.

2. For the second equation, we can rearrange it into slope-intercept form (y = mx + b):
\[
24x - 4y = 96
\]
\[
-4y = -24x + 96
\]
\[
4y = 24x - 96
\]
\[
y = 6x - 24
\]
In this equation, the slope is 6.

Now we compare the slopes:
- The first line has a slope of 4.
- The second line has a slope of 6.

Since the slopes are different, the lines are not parallel.

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