Question

3.
Are the graphs of the lines in the pair parallel? Explain.

y = 5x + 6
–18x + 3y = –54

Answer 1

To determine if the graphs of the lines in the given pair are parallel, we need to find the slopes of both lines and compare them.

1. **First Line:**
The equation of the first line is given in slope-intercept form:

\[
y = 5x + 6
\]

The slope (m) of this line is 5.

2. **Second Line:**
The second line is given in standard form:

\[
-18x + 3y = -54
\]

To find the slope, we can convert this to slope-intercept form (y = mx + b). Start by isolating \(y\):

\[
3y = 18x - 54
\]
\[
y = 6x - 18
\]

The slope of the second line is 6.

3. **Comparison of Slopes:**
Now we compare the slopes:
- Slope of the first line: 5
- Slope of the second line: 6

Since the slopes are different (5 ≠ 6), the lines are **not parallel**.

### Conclusion:
The graphs of the lines in the pair are not parallel because their slopes are different.