Question

Identifying Parallel Lines
Which lines are parallel to the graph of 4x – y = 6? Check all that apply.

x – 4y = –12
y – 2 = –4(x + 1)
y + 1 = 4(x – 2)
y = 4x + 11
y = x – 3
8x – 2y = 6

Answer 1

First line: 4x − y = 6 → y = 4x − 6, so slope = 4.

Convert each candidate to y = mx + b:

- x − 4y = −12 → y = (1/4)x + 3 (slope 1/4) → not parallel
- y − 2 = −4(x + 1) → y = −4x − 2 (slope −4) → not parallel
- y + 1 = 4(x − 2) → y = 4x − 9 (slope 4) → parallel
- y = 4x + 11 (slope 4) → parallel
- y = x − 3 (slope 1) → not parallel
- 8x − 2y = 6 → y = 4x − 3 (slope 4) → parallel

Lines parallel to 4x − y = 6 are:
y + 1 = 4(x − 2), y = 4x + 11, and 8x − 2y = 6.