Determine whether the pair of lines is​ parallel, perpendicular, or neither.
y equals eight thirds x plus 12
y equals eight thirds x minus 12
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Part 1
Choose the correct answer below.
A.Neither
Neither
B.Perpendicular
Perpendicular
C.Parallel
Parallel
Choose the

The equations of the two lines are:

1. \( y = \frac{8}{3}x + 12 \)
2. \( y = \frac{8}{3}x - 12 \)

To determine whether the lines are parallel, perpendicular, or neither, we examine the slopes of the two lines. For lines in the form \( y = mx + b \), the slope is given by \( m \).

Both lines have the same slope \( \frac{8}{3} \). Since the slopes are equal, the lines are **parallel**.

Thus, the correct answer is:

**C. Parallel**

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Would you like more details on parallel and perpendicular lines or have any questions?

Here are some related questions to explore further:

1. How do you find the slope of a line given two points?
2. What does it mean for two lines to be perpendicular in terms of their slopes?
3. How can you tell if two lines will never intersect?
4. How do changes in the y-intercept affect parallel lines?
5. What happens to two lines' slopes if they are neither parallel nor perpendicular?

**Tip:** For two lines to be perpendicular, their slopes must be negative reciprocals of each other.

Determine whether the pair of lines is parallel, perpendicular, or neither.

y = 8/3x + 12
y = 8/3x - 12

This problem involves determining whether the lines y = 8/3x + 12 and y = 8/3x - 12 are parallel, perpendicular, or neither. Learn about slope calculations and how to verify conditions for parallel and perpendicular lines. Suitable for students in Grades 8-10.

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