Let's analyze the problem from the image you uploaded.

You are asked to compare the slope of two linear equations:

1. $3x - 11y = 8$
2. $y = \frac{3}{11}x - 6$

Step 1: Convert the first equation to slope-intercept form.

The slope-intercept form of a line is $y = mx + b$, where $m$ represents the slope.

For the first equation, $3x - 11y = 8$, solve for $y$:

$3x - 11y = 8$ $-11y = -3x + 8$ $y = \frac{3}{11}x - \frac{8}{11}$

Now the first equation is in slope-intercept form: $y = \frac{3}{11}x - \frac{8}{11}$

Step 2: Compare the slopes

The slope of the first equation is $\frac{3}{11}$, and the slope of the second equation $y = \frac{3}{11}x - 6$ is also $\frac{3}{11}$.

Since the slopes are the same, the two lines are parallel.

Conclusion:

The correct answer is parallel.

Would you like more details or have any other questions?

Here are five questions to extend your understanding:

1. What happens when the slopes of two lines are different?
2. How can you find the slope when an equation is not in slope-intercept form?
3. What does it mean for two lines to be perpendicular in terms of their slopes?
4. How do you identify whether lines are parallel or intersecting from their equations?
5. Can two lines have the same slope and still not be parallel?

Tip: When two lines are parallel, their slopes are always equal.