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 y-intercepts are different.


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


No, since the slopes are different.

Answers

Answered by GPT-4o mini
To determine whether the graphs of the given lines are parallel, we need to find their slopes.

1. The first line is given in slope-intercept form:
\[
y = 4x - 4
\]
Here, the slope (m) is 4.

2. The second line is given in standard form:
\[
24x - 4y = 96
\]
We can convert it to slope-intercept form (y = mx + b) by solving for y:

\[
-4y = -24x + 96
\]
Dividing each term by -4:
\[
y = 6x - 24
\]
Here, the slope is 6.

Next, we compare the slopes of the two lines:

- The first line has a slope of 4.
- The second line has a slope of 6.

Since the slopes (4 and 6) are different, the lines are **not parallel**.

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

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